Section: 16-1 Topic: Superposition of Waves Type: Factual



| |Section: 7–1 Topic:  Superposition of Waves Type:  Factual |

| |The interference of waves refers to the |

|A) |slowing down of one wave in the presence of another. |

|B) |resultant disturbance of two or more waves at every point in the medium. |

|C) |change in wavelength that occurs when two waves cross one another. |

|D) |phase change of 180º that occurs on reflection of a wave at a fixed end. |

|E) |ability of waves to go around corners. |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| | |

| |[pic] |

| |In graph A, two waves are shown at a given instant. What is the number of the curve in graph B that represents the wave |

| |resulting from the superposition of the two waves in A at this instant? |

|A) |1 |D) |The resultant is zero for all values of x. |

|B) |2 |E) |None of these represent the wave. |

|C) |3 | | |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| | |

| |[pic] |

| |Sketch A shows two identical pulses traveling in opposite directions along a string, each with a velocity of 1.0 cm/s. After |

| |4.0 s, the string will look like which of the other sketches? |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Factual |

| |Two wave trains of the same frequency are traveling in opposite directions down a string. When they meet, these wave trains |

| |will not |

|A) |be described by the principle of superposition. |

|B) |reflect from each other. |

|C) |pass through one another. |

|D) |continue to carry energy. |

|E) |remain transverse. |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Tuning fork A has a frequency of 440 Hz. When A and a second tuning fork B are struck simultaneously, four beats per second are|

| |heard. When a small mass is added to one of the tines of B, the two forks struck simultaneously produce two beats per second. |

| |The original frequency of tuning fork B was |

| |A) 448 Hz B) 444 Hz C) 438 Hz D) 436 Hz E) 432 Hz |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |The air columns in two identical pipes vibrate at frequencies of 150 Hz. The percentage of change needed in the length of one |

| |of the pipes to produce 3 beats per second is |

| |A) 1% B) 2% C) 3% D) 4% E) 5% |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |Two loudspeakers S1 and S2, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener L directly in|

| |front of speaker S1 notices that the intensity is a minimum when she is 4.0 m from that speaker (see figure). What is the |

| |lowest frequency of the emitted tone? The speed of sound in air is 340 m/s. |

| |A) 85 Hz B) 0.17 kHz C) 0.26 kHz D) 0.34 kHz E) 0.51 kHz |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |If two identical waves with the same phase are added, the result is |

|A) |a wave with the same frequency but twice the amplitude. |

|B) |a wave with the same amplitude but twice the frequency. |

|C) |a wave with zero amplitude. |

|D) |a wave with zero frequency. |

|E) |This problem cannot be solved without knowing the wavelengths of the two waves. |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |Two loudspeakers S1 and S2, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener directly in |

| |front of speaker S1 notices that the intensity is a minimum when she is 4.0 m from that speaker (see figure). The listener now |

| |walks around speaker S1 in an arc of a circle, staying 4.0 m from that speaker but increasing her distance from the other |

| |speaker. How far is she from speaker S2 when she notices the first maximum in the sound intensity? The speed of sound in air |

| |is 340 m/s. |

| |A) 4.5 m B) 5.0 m C) 5.5 m D) 6.0 m E) 6.5 m |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |If two identical waves with a phase difference of 6π are added, the result is |

|A) |a wave with the same frequency but twice the amplitude. |

|B) |a wave with the same amplitude but twice the frequency. |

|C) |a wave with zero amplitude. |

|D) |a wave with zero frequency. |

|E) |This problem cannot be solved without knowing the wavelengths of the two waves. |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |If two identical waves with a phase difference of 3π are added, the result is |

|A) |a wave with the same frequency but twice the amplitude. |

|B) |a wave with the same amplitude but twice the frequency. |

|C) |a wave with zero amplitude. |

|D) |a wave with an intensity equal to the sum of the intensities of the two waves. |

|E) |This problem cannot be solved without knowing the wavelengths of the two waves. |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |What is the phase difference at any given instant between two points on a wave which are 1.52 m apart if the wavelength of the |

| |wave is 2.13 m? |

| |A) 0.430 rad B) 2.70 rad C) 4.48 rad D) 44.0 rad E) 119 rad |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s. The minimum distance between two points with a |

| |phase difference of 60º is |

| |A) 0.040 m B) 0.12 m C) 0.14 m D) 0.24 m E) 25 m |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |Two waves with the same frequency and wavelength but with different amplitudes are added. If A1 = 2A2 and the waves are 180º |

| |out of phase, then the amplitude of the resultant wave is |

|A) |zero. |D) |equal to A1 + A2. |

|B) |the same as A1. |E) |coherent. |

|C) |the same as A2. | | |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Two whistles produce sounds with wavelengths 3.40 m and 3.30 m. What is the beat frequency produced? (the speed of sound is |

| |340 m/s) |

| |A) 0.1 Hz B) 1.0 Hz C) 2.0 Hz D) 3.0 Hz E) 4.0 Hz |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Middle C on a piano has a frequency of 262 Hz. Sometimes it is said that middle C is actually 28 = 256 Hz, and tuning forks are|

| |made with this frequency. How many beats per second would be heard if such a tuning fork were sounded simultaneously with the |

| |middle C of a (well-tuned) piano? |

| |A) 3 B) 6 C) 12 D) 4 E) 8 |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |A violinist is tuning the A string on her violin by listening for beats when this note is played simultaneously with a tuning |

| |fork of frequency 440 Hz. She hears a beat frequency of 4 Hz. She notices that, when she increases the tension in the string |

| |slightly, the beat frequency decreases. What was the frequency of the mistuned A string? |

| |A) 448 Hz B) 444 Hz C) 436 Hz D) 432 Hz E) 438 Hz |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Two trumpet players are both playing a pitch with a frequency of 440 Hz, corresponding to the musical pitch A above middle C. |

| |However, one of the trumpet players is marching away from you so that you hear a beat frequency of 4 Hz from the two trumpets. |

| |With what speed is the departing trumpet player moving away from you? (The speed of sound in air is 340 m/s) |

| |A) 3.12 m/s B) 3.09 m/s C) 3.06 m/s D) 3.00 m/s E) 2.95 m/s |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork, he hears 4 beats each second. The |

| |frequency of the piano's A is |

| |A) 440 Hz B) 444 Hz C) 880 Hz D) 436 Hz E) either 436 Hz or 444 Hz |

|Ans: |E |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |Two tones of equal amplitude but slightly different frequencies are emitted by a sound source. This gives rise to |

|A) |standing waves. |D) |beats. |

|B) |destructive interference. |E) |amplification. |

|C) |constructive interference. | | |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| | |

| |[pic] |

| |At P1, the waves from sources S1 and S2 shown in the figure |

|A) |are out of phase. |

|B) |have a path difference of one wavelength. |

|C) |have a path difference of two wavelengths. |

|D) |are interfering destructively. |

|E) |None of these is correct. |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| | |

| |[pic] |

| |At P2 the waves from sources S1 and S2 shown in the figure |

|A) |are in phase. |

|B) |have a path difference of one wavelength. |

|C) |have a path difference of one-half wavelength. |

|D) |are interfering constructively. |

|E) |None of these is correct. |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| | |

| |[pic] |

| |The sources S1 and S2 are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path|

| |difference of two wavelengths is |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |One source of sound is at A and another is at B. The two sources are in phase. The distance AB = 10.0 m. The frequency of the |

| |sound waves from both sources is 1000 Hz, and both have the same amplitude. The speed of sound in air is 330 m/s. A receiver |

| |is at point C, and AB is perpendicular to AC. The greatest distance AC for which the signal at C is a minimum is |

| |A) 33.0 cm B) 152 m C) 330 m D) 303 m E) 100 m |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is |

| |A) 2.0 mm B) 1.8 mm C) 1.4 mm D) 1.0 mm E) 0.83 mm |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is |

|A) |π radians. |D) |π/8 radians. |

|B) |π/2 radians. |E) |π/16 radians. |

|C) |π/4 radians. | | |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is |

|A) |π radians. |D) |π/8 radians. |

|B) |π/2 radians. |E) |π/16 radians. |

|C) |π/4 radians. | | |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is |

| |A) 2.0 mm B) 1.8 mm C) 1.4 mm D) 1.0 mm E) zero |

|Ans: |E |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to |

| |A) 2.0 mm B) 1.8 mm C) 1.4 mm D) 1.0 mm E) zero |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to |

|A) |3.1 radians. |D) |2.4 radians. |

|B) |1.6 radians. |E) |0.2 radians. |

|C) |1.1 radians. | | |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to |

|A) |1.0 radians. |D) |2.5 radians. |

|B) |1.5 radians. |E) |3.0 radians. |

|C) |2.0 radians. | | |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| | |

| |[pic] |

| |The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to |

| |A) 2.0 mm B) 1.8 mm C) 1.4 mm D) 1.0 mm E) zero |

|Ans: |B |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound |

| |intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator. |

| |A) 256 Hz B) 1024 Hz C) 512 Hz D) 341 Hz E) 683 Hz |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Conceptual |

| |Two wave trains travel on a string under a constant tension T. Which of the following statements is NOT correct? |

|A) |The two waves can have different speed. |

|B) |The two waves can have different frequency. |

|C) |The two waves can have different wavelength. |

|D) |The superposition principle applies for the two waves. |

|E) |At any point on the string, the resultant amplitude is the algebraic sum of the amplitudes of the two waves. |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Two sound waves, one wave is given by y1 = po sin (kx – ωt) and the other by y2 = po sin (kx – ωt + π/2). The amplitude |

| |resulting from the interference of the two waves is |

| |A) 2po B) [pic] C) 1.25po D) [pic] E) 0 |

|Ans: |D |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Two sound waves, one wave is given by y1 = po sin (kx – ωt) and the other by y2 = po sin (kx – ωt + π/4). The phase constant |

| |resulting from the interference of the two waves is |

| |A) (/8 B) (/4 C) (/2 D) ( E) 0 |

|Ans: |A |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Numerical |

| |Two sound waves, one wave is given by y1 = po sin (ω1t), and the other by y2 = po sin (ω2t), where ω1 differs from ω2 by a |

| |rad/s. The maximum sound intensity of the beat frequency is |

| |A) po2 B) 2po2 C) 4po2 D) 8po2 A) 0 |

|Ans: |C |

| |Section: 7–1 Topic:  Superposition of Waves Type:  Factual |

| |Two sources are said to be coherent if |

|A) |they are of the same frequency and has a phase of zero. |

|B) |they are of the same frequency and maintain a constant non-zero phase. |

|C) |they are of the same intensity but different frequency and has a phase of zero. |

|D) |they are of the same intensity but different frequency and maintain a constant non-zero phase. |

|E) |(A) and (B) |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |One wave moves to the right and a second wave (reflected) moves to the left to form a stationary wave. At which point(s) does |

| |the stationary wave have a node? |

| |A) 1 B) 3 and 5 C) 2 D) 4 and 6 E) 2, 4, and 6 |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a |

| |standing wave is set up in the string. One will observe a node at position |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a |

| |standing wave will be set up in the string. One of the antinodes in the standing wave will be found at position |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The two progressive waves are moving with equal velocities and wavelengths but in opposite directions in the string. Which of |

| |the following gives all of the points that will be nodes in the resultant standing wave? |

|A) |2, 4, 6, 8, and 10 |D) |3 and 7 |

|B) |2, 6, and 10 |E) |1, 3, 5, 7, and 9 |

|C) |1, 5, and 9 | | |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string whose length is 1 m is fixed at both ends and vibrates according to the equation |

| | |

| | |

| |y(x, t) = 0.04 sin πx cos 2πt |

| | |

| | |

| |where the units are SI. The total number of nodes exhibited by the string is |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |If the amplitude of a standing wave is doubled, the energy in the wave increases by a factor of |

| |A) [pic] B) [pic] C) 1 D) 2 E) 4 |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental |

| |frequency of the string is multiplied by |

| |A) 1 B) 2 C)[pic] D) [pic] E) [pic] |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The fundamental frequency of a vibrating string is f1. If the tension in the string is doubled, the fundamental frequency |

| |becomes |

| |A) f1/2 B) [pic] [pic] C) f1 D) [pic] E) 2f1 |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The fundamental frequency of a vibrating string is f1. If the tension in the string is increased by 50% while the linear |

| |density is held constant, the fundamental frequency becomes |

| |A) f1 B) 1.2f1 C) 1.5f1 D) 1.7f1 E) 2f1 |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The fundamental frequency of a vibrating string is f1. If the tension in the string is decreased by 50% while the linear |

| |density is held constant, the fundamental frequency becomes |

| |A) 0.5f1 B) 0.7f1 C) 0.9f1 D) f1 E) None of these is correct. |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The fundamental frequency of a vibrating string is f1. If the tension in the string is quadrupled while the linear density is |

| |held constant, the fundamental frequency becomes |

| |A) f1 B) 1.2f1 C) 1.5f1 D) 1.7f1 E) 2f1 |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The figure shows several modes of vibration of a string fixed at both ends. The mode of vibration that represents the fifth |

| |harmonic is |

| |A) 1 B) 2 C) 3 D) 4 E) None of these is correct. |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Factual |

| |Which of the following equations represents a standing wave? (The symbols have their usual meaning.) |

|A) |[pic] |C) |[pic] |

|B) |[pic] |D) |[pic] |

|E) |(B) and (D) | | |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A standing wave is shown in the figure on the right. If the period of |[pic] |

| |the wave is T, the shortest time it takes for the wave to go from the | |

| |solid curve to the dashed curve is | |

| |A) T/4 B) T/3 C) T/2 D) 3T/4 E) None of these is correct. |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A string of linear density ( and length L is under a constant |[pic] |

| |tension T = mg. One end of the string is attached to a tunable | |

| |harmonic oscillator. A resonant standing wave is observed | |

|A) |at any frequency. |

|B) |when the frequency [pic] where n = 1, 2, 3, ... |

|C) |when the frequency [pic] where n = 1, 2, 3, ... |

|D) |when the frequency [pic] where n = 1, 2, 3, ...and vs is the speed of sound. |

|E) |unable to tell |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A standing wave is created by oscillating a taut string at a frequency|[pic] |

| |that corresponds to one of the resonant frequencies. The amplitude of | |

| |the antinodes is very much larger than the amplitude of the | |

| |oscillator. Does this violate the conservation of energy principle? | |

| |Explain why. | |

|A) |Yes, since E is proportional to amplitude squared. |

|B) |Yes, since there is large kinetic energy of the string, and this is much bigger than the energy from the oscillator. |

|C) |No, energy from waves does not obey the conservation of energy principle in the first place. |

|D) |No, the energy at the antinodes builds up after the first few cycles, after which the dissipation due to friction equals |

| |the energy supplied by the oscillator. |

|E) |Whether it obeys the conservation of energy principle depends on the tension in the string. |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A microphone is placed at the node of a standing sound wave. What does the microphone pick up? |

|A) |A constant and very high intensity sound. |

|B) |A constant and very low intensity sound. |

|C) |A varying high intensity sound. |

|D) |A varying low intensity sound. |

|E) |Unable to tell. |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |Four pendulums are hung from a light rod that is free to rotate about its long axis. The |[pic] |

| |pendulums have lengths L, 2L, L/2 and L, and masses m, m/2, 2m and 4m respectively. Pendulum| |

| |1 is set to swing at its natural frequency. Which of the other three will, over time, also | |

| |oscillate at the same frequency? | |

|A) (2) B) (3) C) (4) D) (2) and (3) E) all three |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |In a vibrating-string experiment, three loops are observed |[pic] |

| |between points A and B when the mass on one end of the string | |

| |is 100 g. The number of loops between A and B can be changed | |

| |to two by replacing the 100-g mass with a mass of | |

| |A) 150 g B) 225 g C) 44.4 g D) 66.7 g E) 300 g |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string 2.0 m long has a mass of 2.4 × 10–2 kg. When fixed at both ends, it vibrates with a fundamental frequency of 150 Hz. |

| |The speed of a transverse wave in the string is |

| |A) 3.6 m/s B) 75 m/s C) 0.30 km/s D) 0.60 km/s E) 0.63 km/s |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string 2.0 m long has a mass of 2.4 × 10–2 kg. When fixed at both ends, it vibrates with a fundamental frequency of 150 Hz. |

| |The frequency of the third harmonic of this fundamental is |

| |A) 50 Hz B) 75 Hz C) 0.15 kHz D) 0.45 kHz E) 1.1 kHz |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |A stationary wave of amplitude A and period T exists in a rope. At a particular instant, the configuration of the rope is as |

| |shown. At an instant [pic]T later, the configuration of the rope is |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| | |

| |[pic] |

| |A string is connected to a tuning fork whose frequency is 80.0 Hz and is held under tension by 0.500 kg. The tuning fork causes|

| |the string to vibrate as shown. The mass per unit length for the string is |

|A) |9.45 × 10–4 kg/m |D) |6.00 × 10–3 kg/m |

|B) |6.80 × 10–3 kg/m |E) |3.85 × 10–2 kg/m |

|C) |4.34 kg/m | | |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |A stretched string is fixed at points 1 and 5. When it is vibrating at the second harmonic frequency, the nodes of the standing|

| |wave are at points |

| |A) 1 and 5. B) 1, 3, and 5. C) 1 and 3. D) 2 and 4. E) 1, 2, 3, 4, and 5. |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |A stretched string is fixed at points 1 and 5. When it is vibrating in its first harmonic frequency, the nodes are at points |

|A) |1 and 5 only. |D) |2, 3, and 4. |

|B) |1, 3, and 5. |E) |1, 2, 3, 4, and 5. |

|C) |2 and 4. | | |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A string fixed at both ends is driven by a tuning fork to produce standing waves. If the tension in the string is increased, |

|A) |the frequency increases. |

|B) |the frequency decreases and the wave velocity remains constant. |

|C) |the wavelength decreases. |

|D) |the wave velocity increases. |

|E) |the wave velocity decreases. |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | The figure shows a standing wave in a pipe that is closed at |[pic] |

| |one end. The frequency associated with this wave pattern is | |

| |called the | |

|A) |first harmonic. |D) |fourth harmonic. |

|B) |second harmonic. |E) |fifth harmonic. |

|C) |third harmonic. | | |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |Of the sound sources shown, that which is vibrating with its first harmonic is |

|A) |the whistle. |D) |the vibrating rod. |

|B) |the organ pipe. |E) |None of these is correct. |

|C) |the vibrating string. | | |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |Of the sound sources shown, that which is vibrating with its first harmonic is the |

|A) |whistle. |D) |vibrating rod. |

|B) |organ pipe. |E) |vibrating spring. |

|C) |vibrating string. | | |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |When an organ pipe, which is closed at one end only, vibrates with a frequency that is three times its fundamental (first |

| |harmonic) frequency, |

|A) |the sound produced travels at three times its former speed. |

|B) |the sound produced is its fifth harmonic. |

|C) |beats are produced. |

|D) |the sound produced has one-third its former wavelength. |

|E) |the closed end is a displacement antinode. |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| | |

| |[pic] |

| |The air in a closed organ pipe vibrates as shown. The length of the pipe is 3.0 m. The frequency of vibration is 80 Hz. The |

| |speed of sound in the pipe is approximately |

| |A) 80 m/s B) 0.16 km/s C) 0.24 km/s D) 0.32 km/s E) 0.96 km/s |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. |

| |As the water level is lowered, consecutive maxima in intensity are observed at intervals of about |

| |A) 12.9 cm B) 19.4 cm C) 25.8 cm D) 51.7 cm E) 194 cm |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. |

| |As the water level is lowered, consecutive maxima in intensity are observed at intervals of about |

| |A) 7.65 cm B) 15.3 cm C) 23.0 cm D) 30.6 cm E) 53.6 cm |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The air column in an organ pipe, which is closed at one end, is vibrating in such a way as to produce the second harmonic. A |

| |pressure node and displacement node, respectively, occur at |

| |A) 1 and 3 B) 1 and 5 C) 7 and 4 D) 7 and 5 E) 5 and 3 |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A string fixed at both ends is vibrating in a standing wave. There are three nodes between the ends of the string, not |

| |including those on the ends. The string is vibrating at a frequency that is its |

|A) |fundamental. |D) |fourth harmonic. |

|B) |second harmonic. |E) |fifth harmonic. |

|C) |third harmonic. | | |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |On a standing-wave pattern, the distance between two consecutive nodes is d. The wavelength is |

| |A) d/2 B) d C) 3d/2 D) 2d E) 4d |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |A stretched string of length L, fixed at both ends, is vibrating in its third harmonic. How far from the end of the string can |

| |the blade of a screwdriver be placed against the string without disturbing the amplitude of the vibration? |

| |A) L/6 B) L/4 C) L/5 D) L/2 E) None of these is correct. |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |In a pipe that is open at one end and closed at the other and that has a fundamental frequency of 256 Hz, which of the following|

| |frequencies cannot be produced? |

|A) |768 Hz |D) |19.7 kHz |

|B) |1.28 kHz |E) |all of these can be produced |

|C) |5.12 kHz | | |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |The fundamental frequency of a pipe that has one end closed is 256 Hz. When both ends of the same pipe are opened, the |

| |fundamental frequency is |

| |A) 64.0 Hz B) 128 Hz C) 256 Hz D) 512 Hz E) 1.02 kHz |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |The standing waves on a string of length L that is fixed at both ends have a speed v. The three lowest frequencies of vibration|

| |are |

|A) |v/L, 2v/L, and 3v/L |D) |L/v, 2L/v, and 3L/v |

|B) |v/2L, v/L, and 3v/2L |E) |λ/3, 2λ/3, and 3λ/3 |

|C) |λ/2, λ, and 3λ/2 | | |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |Standing waves exist in a string of length L that is fixed at one end and free at the other. The speed of the waves on the |

| |string is v. The three lowest frequencies of vibration are |

|A) |v/4L, v/2L, and 3v/4L |D) |v/4L, 3v/4L, and 5v/4L |

|B) |v/2L, v/L, and 3v/2L |E) |λ/3, 2λ/3, and 3λ/3 |

|C) |λ/4, λ/2, and 3λ/4 | | |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |The standing waves in air in a pipe of length L that is open at both ends have a speed v. The frequencies of the three lowest |

| |harmonics are |

|A) |v/L, 2v/L, and 3v/L |D) |L/v, 2L/v, and 3L/v |

|B) |v/2L, v/L, and 3v/2L |E) |λ/3, 2λ/3, and 3λ/3 |

|C) |λ/2, λ, and 3λ/2 | | |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |The standing waves in air in a pipe of length L that is open at one end and closed at the other have a speed v. The frequencies|

| |of the three lowest harmonics are |

|A) |v/4L, v/2L, and 3v/4L |D) |v/4L, 3v/4L, and 5v/4L |

|B) |v/2L, v/L, and 3v/2L |E) |λ/3, 2λ/3, and 3λ/3 |

|C) |λ/4, λ/2, and 3λ/4 | | |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A 1.00 m string fixed at both ends vibrates in its fundamental mode at 440 Hz. What is the speed of the waves on this string? |

| |A) 220 m/s B) 440 m/s C) 660 m/s D) 880 m/s E) 1.10 km/s |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The human vocal tract can be thought of as a tube that is open at one end. If the length of this tube is 17 cm (about average |

| |for an adult male), what are the lowest two harmonics? |

|A) |500 Hz, 1500 Hz |D) |1000 Hz, 3000 Hz |

|B) |500 Hz, 1000 Hz |E) |1500 Hz, 2500 Hz |

|C) |1000 Hz, 2000 Hz | | |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |For a tube of length 57.0 cm that is open at both ends, what is the frequency of the fundamental mode? (the speed of sound in |

| |air is 340 m/s) |

| |A) 149 Hz B) 447 Hz C) 596 Hz D) 298 Hz E) 746 Hz |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string fixed at both ends is 50.0 cm long and has a tension that causes the frequency of its fundamental to be 262 Hz. If the|

| |tension is increased by 4%, what does the fundamental frequency become? |

| |A) 252 Hz B) 257 Hz C) 264 Hz D) 267 Hz E) 272 Hz |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A clarinet, which is essentially a tube that is open at one end, is properly tuned to concert A (440 Hz) indoors, where the |

| |temperature is 20ºC and the speed of sound is 340 m/s. The musician then takes the instrument to play an outdoor concert, where|

| |the temperature is 0ºC and the speed of sound is 331 m/s. What is the frequency of the A played on the cold clarinet? (Ignore |

| |any thermal changes in the body of the clarinet itself.) |

| |A) 417 Hz B) 428 Hz C) 434 Hz D) 445 Hz E) 451 Hz |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |Sound has a velocity of 335 m/s in air. For an air column that is closed at both ends to resonate to a frequency of 528 Hz, the|

| |length of the air column could be |

| |A) 79.2 cm B) 55.5 cm C) 47.5 cm D) 31.7 cm E) 15.8 cm |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| | |

| |[pic] |

| |The sound wave in an organ tube has a wavelength that is equal to the distance between |

|A) |A and B. |D) |the antinodes farthest apart. |

|B) |A and C. |E) |None of these is correct. |

|C) |the nodes farthest apart. | | |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The third harmonic of a tube closed at one end is 735 Hz. If the speed of sound in air is 335 m/s, the length of the tube must |

| |be |

| |A) 11.6 cm B) 22.9 cm C) 34.1 cm D) 45.7 cm E) 57.3 cm |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The ratio of the fundamental frequency (first harmonic) of an open pipe to that of a closed pipe of the same length is |

| |A) 2:1 B) 7:8 C) 4:5 D) 3:2 E) 1:2 |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where |

| |the units are SI. The amplitudes of the traveling wave that result in this standing wave are |

|A) |0.04 m |

|B) |0.08 m |

|C) |0.02 m |

|D) |0.16 m |

|E) |impossible to tell given this information about the standing wave. |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where |

| |the units are SI. The wavelength of this wave is |

|A) |6.00 m |

|B) |1.05 m |

|C) |600 m |

|D) |0.010 m |

|E) |impossible to tell given this information about the standing wave. |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where |

| |the units are SI. The speed of the traveling waves that result in this standing wave is |

|A) |6.00 m |

|B) |1.05 m |

|C) |600 m |

|D) |0.010 m |

|E) |impossible to tell given this information about the standing wave. |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where |

| |the units are SI. The distance between successive nodes on the string is |

|A) |0.24 m |

|B) |0.08 m |

|C) |0.02 m |

|D) |0.52 m |

|E) |impossible to tell given this information about the standing wave. |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found |

| |at 558 Hz and the next one at 744 Hz. What is the fundamental frequency of the string? |

| |A) 558 Hz B) 372 Hz C) 93 Hz D) 186 Hz E) none of the above |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found |

| |at 558 Hz and the next one at 744 Hz. To what harmonic does the 558 Hz resonance correspond? |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found |

| |at 558 Hz and the next one at 744 Hz. What is the length of the wire? |

| |A) 0.8 m B) 1.6 m C) 3.2 m D) 1.2 m E) 0.4 m |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A wire of mass 1.1 g is under a tension of 100 N. If its third overtone is at a frequency of 750 Hz, calculate the length of the|

| |wire. |

| |A) 72 cm B) 101 cm C) 36 cm D) 65 cm E) None of the above |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A vibrating tuning fork is held above a tube filled with water. The first two resonances occur when the water level is lowered |

| |by 14.2 cm and 44.2 cm from the top of the tube. If there is a small end correction that adds a small extra length ΔL? to the |

| |effective length of the air column, calculate the frequency of the tuning fork. Assume the speed of sound to be 330 m/s. |

| |A) 560 Hz B) 581 Hz C) 550 Hz D) 1100 Hz E) 1120 Hz |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A vibrating tuning fork of 850 Hz is held above a tube filled with water. The first and third resonances occur when the water |

| |level is lowered by 8.8 cm and 47.6 cm from the top of the tube. If there is a small end correction that adds a small extra |

| |length ΔL to the effective length of the air column, calculate ΔL. Assume the speed of sound to be 330 m/s. |

| |A) 0.2 cm B) 0.9 cm C) 0.4 cm D) 0.6 cm E) 1.1 cm |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A vibrating tuning fork of 725 Hz is held above a tube filled with water. Successive resonances are heard when the water level |

| |is lowered by 11.5 cm and 34.5 cm from the top of the tube. Calculate a value for the speed of sound. (Hint: remember the small |

| |end correction ΔL at the top of the tube.) |

| |A) 333 m/s B) 343 m/s C) 325 m/s D) 315 m/s E) 338 m/s |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Conceptual |

| |Two pipes closed at one end of length L1 and L2 are excited at their resonant frequencies. If the beat period is Bf Hz, then the|

| |velocity of sound is given by: |

|A) |Bf × L1 × L2 / (4L1 − 4L2) |D) |4 × Bf × L1 × L2 / (L1 − L2) |

|B) |4 × Bf × L1 × L2 / (4L1 − 4L2) |E) |4 × Bf × L1 × L2 / (L1 + L2) |

|C) |16 × Bf × L1 × L2 / (4L1 + 4L2) | | |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A vibrating tuning fork of 300 Hz is held above a tube filled with water. The first resonance is heard when the water level is |

| |lowered by 26.1 cm. A second tuning fork of 400 Hz is held above the tube, and its first resonance occurs when the water level |

| |is lowered by 19.3 cm from the top. Calculate a value for the speed of sound. (Hint: remember the small end correction ΔL at the|

| |top of the tube.) |

| |A) 333 m/s B) 343 m/s C) 325 m/s D) 315 m/s E) 338 m/s |

|Ans: |C |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A guitar string of length 105 cm is in resonance with a tuning fork of frequency f. Using the fret board the length of the |

| |string is shortened by 1.5 cm while keeping the tension in the string constant. Now a beat frequency of 10 Hz is heard between |

| |the string and the tuning fork. What is the frequency of the tuning fork? |

| |A) 230 Hz B) 1380 Hz C) 345 Hz D) 690 Hz E) none of the above |

|Ans: |D |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |Wire A is the same mass per unit length as wire B. However wire A is twice as long as wire B and has three times as much tension|

| |on it. Calculate the fundamental frequency of wire A divided by wire B. |

| |A) 0.87 B) 0.66 C) 0.43 D) 0.75 E) 1.50 |

|Ans: |A |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |What is the third harmonic of an open-both-ends organ pipe of length 1.5 m? Assume the speed of sound to be 340 m/s. |

| |A) 229 Hz B) 340 Hz C) 457 Hz D) 686 Hz E) none of the above |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A piano tuner hears a beat every 0.33 seconds when he hits a note and compares it to his reference tone at 163 Hz. What is the |

| |lowest possible frequency of the piano note? |

| |A) 44.9 Hz B) 166.0 Hz C) 162.7 Hz D) 163.3 Hz E) 160.0 Hz |

|Ans: |E |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |Two identical loudspeakers are driven in phase by the same amplifier. The speakers are positioned a distance of 3.2 m apart. A |

| |person stands 4.1 m away from one speaker and 4.8 m away from the other. Calculate the second lowest frequency that results in |

| |destructive interference at the point where the person is standing. Assume the speed of sound to be 340 m/s. |

| |A) 245 Hz B) 735 Hz C) 1225 Hz D) 490 Hz E) 1470 Hz |

|Ans: |B |

| |Section: 7–2 Topic:  Standing Waves Type:  Numerical |

| |A pipe produces successive harmonics at 300 Hz and 350 Hz. Calculate the length of the pipe and state whether it is closed at |

| |one end or not. Assume the speed of sound to be 340 m/s. |

|A) |1.7 m |

| |closed one end |

| | |

|B) |3.4 m |

| |open both ends |

| | |

|C) |4.0 m |

| |closed one end |

| | |

|D) |8.0 m |

| |closed one end |

| | |

|E) |4.0 m |

| |open both ends |

| | |

|Ans: |B |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| |The reason we can tell the difference between a trumpet and a clarinet when they both play the same pitch is that they have |

|A) |the same overtones. |D) |different waveforms. |

|B) |the same harmonics. |E) |harmonic syntheses. |

|C) |different fundamental frequencies. | | |

|Ans: |D |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| |The electronic music synthesizer is based on the results of |

|A) |harmonic synthesis. |D) |Fourier analysis. |

|B) |overtones. |E) |all of these factors. |

|C) |tone quality. | | |

|Ans: |E |

| |Section: 7–3 Topic: Additional Topics Type:  Factual |

| |A string with length L is fixed on both ends. If λo = 2L and fo = v/λο, the wave function |[pic] |

| |for the harmonic shown is | |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|Ans: |E |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| | |

| |[pic] |

| |The complex wave whose frequency spectrum is shown in the figure is made up of waves whose frequencies are |

|A) |1, 2, and 4. |D) |1 and 4. |

|B) |100, 200, and 400. |E) |100 and 400. |

|C) |100, 100, and 400. | | |

|Ans: |B |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| | |

| |[pic] |

| |The complex wave whose frequency spectrum is shown in the figure is made up of waves whose relative amplitudes are |

|A) |1, 2, and 4. |D) |200 and 400. |

|B) |100, 200, and 400. |E) |1 and 2. |

|C) |1 and 4. | | |

|Ans: |A |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| | |

| |[pic] |

| |The frequency spectrum of the composite wave 1 + 3 + 5 shown is best represented by |

| |[pic] |

| |A) 1 B) 2 C) 3 D) 4 E) 5 |

|Ans: |E |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| | |

| |[pic] |

| |An examination of this frequency spectrum allows you to conclude that |

|A) |the odd harmonics 1 through 19 are present in the composite wave. |

|B) |the even harmonics 2 through 20 are present in the composite wave. |

|C) |the amplitudes of the component waves are equal. |

|D) |the wave form is a simple sinusoid. |

|E) |None of these is correct. |

|Ans: |A |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| |The three curves show the harmonics of a pipe that is closed one end and |[pic] |

| |open the other end. The fundamental frequency is fo. The three harmonics | |

| |are | |

|A) |fo, 2fo, 3fo |D) |fo, 3fo, 4fo |

|B) |fo, 5fo, 7fo |E) |fo, 6fo, 8fo |

|C) |fo, 4fo, 6fo | | |

|Ans: |B |

|Use the figure to the right to answer the next two problems. |[pic] |

| | |

|The graph shows three harmonics. | |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| |The frequency spectrum of the composite wave is best represented by |

| |[pic] |[pic] |[pic] |[pic] |

| |A) |B) |C) |D) |

| |E) None of the above |

|Ans: |B |

| |Section: 7–3 Topic: Additional Topics Type:  Conceptual |

| |If fo is the fundamental frequency, the three harmonics and their relative intensities can best be written as |

|A) |fo, 2fo, 3fo, and 2:1:0.5 |D) |fo, 3fo, 4fo, and 2:1:0.5 |

|B) |fo, 3fo, 5fo, and 2:1:1 |E) |fo, 6fo, 8fo, and 2:1:1 |

|C) |fo, 3fo, 5fo, and 2:1:0.5 | | |

|Ans: |C |

|Use the figure to the right to answer the next two problems. |[pic] |

| | |

|The graph shows a wave pulse of width w = 5 cm and speed v = 100 m/s. | |

| |Section: 7–3 Topic: Additional Topics Type:  Numerical |

| |The duration of the wave pulse is |

| |A) 0.005 s B) 0.0005 s C) 0.001 s D) 0.02 s E) 0.5 s |

|Ans: |B |

| |Section: 7–3 Topic: Additional Topics Type:  Numerical |

| |The range of frequencies is |

| |A) 2000 s[pic]1 B) 200 s[pic]1 C) 1000 s[pic]1 D) 50 s[pic]1 E) 5 s[pic]1 |

|Ans: |A |

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