Topic #16



Topic #16(. Sound, A Wave Phenomenon

1. Sound Waves

2. Pitch and Loudness

3. Doppler Effect

4. Sources of Sound

5. Resonance

6. Detection of Sound

7. The Quality of Sound

Notes should include:

Sound Waves: Sound is a longitudinal wave. The molecular disturbance in the air is parallel to the forward motion of the wave. This wave of pressurized (air molecules compressed up against one another) air oscillates about an average value. This average value is the average atmospheric pressure in the environment in which the sound waves are being transmitted. The frequency of a sound wave is the number of "pressure" oscillations produced each second. Sound moves through air as the molecules move colliding with the molecules next to them, which in turn move outwards colliding with the next set of molecules, etc.. The speed of sound is a function of the density of the medium. In air this means that the temperature and pressure of the air affect the speed of the wave. This speed is equal to 343 m/s at one atmosphere of pressure and room temperature. What would this value be in km/h? What would it be in mph (miles per hour)?

Sound travels through solids and liquids at a faster rate than in gases. Sound will not travel through a vacuum, because sound requires a medium to travel through. In movies a sound should not be heard when something explodes at a distance in the vacuum of space. On the other hand light should be shown, if any is given off by the explosion, because light does travel in a vacuum.

Sound can and does reflect off of objects. An echo is the result of a sound wave bouncing off of a barrier and returning towards the source of the sound. Sound waves experience diffraction. They can pass through small openings and spread out into the space beyond the opening. Sound is also observed to bend around corners, which also an example of diffraction. Sound waves can and often do experience interference. You have probably heard two different sources of sound at the same time and the interference of the sound waves prevented you from hearing either of the sources very clearly. Destructive interference can create problems in theaters, because of the canceling of the waves that occurs at the nodes where the sound waves cancel one another. Sound waves can also experience constructive interference. In this case two sounds will be louder than either sound heard separately. Sound waves do have wavelengths. The wavelength of a sound wave is the distance between consecutive areas of maximum pressure. These regions of maximum pressure would be called the crests of the sound waves, while the troughs would be the regions of low pressure between the regions of high pressure. The human ear is not capable of hearing all sounds. The typical human ear can hear sounds over a range of 20 Hz to 20 kHz.

Pitch and Loudness: The frequency of a wave is called its pitch. Different pitches are identified in music as notes on a musical scale. Knowledge of musical scales go all the way back to Pythagorus. Two notes differ by an octave, if their frequencies are related by a ratio of 2 / 1. For example, a note having a frequency of 440 hz will have as a counterpart one octave higher a note having a frequency of 880 hz. The interval between notes is not the difference in the frequencies, but rather the interval between notes is the ratio of their frequencies. The loudness of a sound is (called the wave's amplitude. The loudness of a sound appears to double if the amplitude of the wave increases by 20 times of what its original value was. The amplitude of a sound that will cause pain is about one trillion times larger than the amplitude of a sound, which is just perceptible to the human ear. Sound intensity is measured on a scale based on the ratio of amplitudes. Intensities are based on the amplitude of sound that can just be heard. This sound is assigned a value of 0 decibels (0 dB). The intensity of a sound 10 times larger than this would have a value on this scale of 10 dB. A sound with an intensity 10 times larger than 10 dB would have a value of 20 dB on this scale.

Doppler Effect: Have you ever noticed how the sound of something appears to change, if the object producing the sound is moving. Try to remember how the pitch of a train horn appears to change as the train approaches a crossing, passes the crossing, and finally moves away from the crossing. If you listen carefully you notice that the pitch of the horn is higher as the train approaches the crossing, but after it has passed the crossing it has a lower pitch. This effect is called the doppler effect. This phenomenon is caused by the fact that when a source of sound is stationary, the sound waves continue to radiate outwards with wavelengths of the same size in all directions. However, when the source of the sound is moving, the waves being emitted in front off it are being compressed (shortened) causing the pitch (frequency) of the wave to rise. On the other hand, as the sound generating object moves the waves emitted behind it are elongated (stretched) causing the pitch of the wave to be lowered. This shifting of the pitch due to the lengthening or shortening of the wave is called the doppler shift.

Sources of Sound: Sound is produced by vibrations in the air caused by a variety of objects which include vibrating vocal cords, musical instruments like the vibrating strings of guitars, and the vibrating cones in the speakers found in a variety of entertainment devices.

Resonance: Ask someone what happens if you remove the mouthpiece of a brass or reed instrument and blow through it. They will tell you not much. The tube must be attached to produce the sound associated with the particular instrument. When such an instrument is played, the air in the tube of the instrument vibrates with the same frequency as the lips of the person or the reed. You could also say that the air in the tube vibrates in resonance with the vibrating lips or reed. The pitch of the instrument is controlled through changing the length of the tube. The length can be changed through opening or closing valves or moving the slide as in the case of a trombone. At the mouthpiece a mixture of frequencies is often created. Which one is "amplified" and thus heard as coming from the instrument is a function of the length of the tube. That a single frequency is only amplified through the use of a tube of a certain length can be demonstrated by using an ordinary tube opened on both ends. Immerse one end in a column of water, such as in graduate cylinder, making the tube a closed end adjustable length tube. The resonating, chamber’s length, that portion of the tube that is empty, can be changed by raising or lowering the tube.

If you use a tuning fork, a devise which can only produce one single frequency (pitch), struck and held above the tube, you can ascertain the optimum length of the tube for that frequency (pitch) by raising or lowering the tube until a maximum volume is produced. The column of air in a tube of correct length produces the most amplification of the sound and, therefore, the loudest sound. Because the amplification is actually a function of the entering wave being in phase with the reflected exiting wave, there will be more than one length of tube that can produce a resonance for a particular frequency (pitch). The tuning fork sends a wave through the air molecules down the tube. This wave is reflected back up the tube by the water. When a reflected wave is at the same point in its oscillations as the wave coming from the tuning fork the generated and reflected (waves reinforce one another producing a standing wave. In this situation the air molecules forming the standing wave do form nodes and antinodes. Nodes are found where the air molecules are observed to be moving as they usually would (no compression) while the antinodes are found where the air molecules are observed to be moving with maximum forward or backwards motion (highest compression). A node is produced at the waters surface because it stops the molecules downward motion and reflects them back upwards. If you move the tube, such that the distance between the top opening near where the tuning fork is being held and the water at the "bottom" of the air filled portion of the tube changes, in effect the length of the tube is changing. As this movement occurs you would note that there is not just one length that produces resonance with a single tuning fork, but rather there is a series of lengths that produce resonance with a single tuning fork (frequency). This occurs because of the positions of nodes and antinodes in the standing wave produced in the tube. Any tube that would produce a standing wave having a node at the surface of the water at the same time there is an antinode at the water's surface would produce resonance. The possible lengths that would result in resonance in a tube with one end closed are described as odd number multiples of one quarter of a wavelength. These lengths include 1 x (l/4), 3 x (l/4), 5 x (l/4), etc.

Tubes open on both ends also show evidence of resonance. In this situation the optimum multiple lengths of a tube resonating when exposed to a particular tuning fork (frequency) are based on even number multiples of one half of a wavelength beginning with one half of a wavelength. These lengths include (l/2), 2 x (l/2), 3 x (l/2), etc..

Detection of Sound: Devices, which detect sound, have to in some way be sensitive to the kinetic energy of the air molecules vibrating around them and convert this energy being received in the form of waves to some other form of energy such as electrical as in the case of the microphone. How a microphone works will require that you do some studying of electricity and magnetism before you tackle the microphone itself. The human ear is an excellent detector of sound. To understand how it detects sound and your brain appears to interpret it as such is beyond the scope of these notes, but information about how the ear functions should prove interesting reading, if you are motivated to pursue this topic.

Sound Quality: Why do musical instruments appear to sound so very different from one another? Suppose we were to ask someone to play middle C on a piano. How would that compare to playing the same note on a guitar, a violin, a trumpet, a saxophone, etc.. This is because most sounds are made of more than one frequency produced simultaneously. The quality of the sound you hear depends on how these frequencies combine, that is, which are more intense than others present. If you listen to people talk about music, you will hear them speak of timbre. Timbre is the quality of a sound.

Did you ever wonder how someone can tune an instrument like a guitar by listening to another instrument like a piano or how a person tunes a piano by listening to a tuning fork? The answer has to due with a concept called beat. In this situation we are defining the word beat as the pulsing variation in loudness, which occurs when two waves very close in frequency are produced simultaneously. Each wave independently has its own amplitude. However, when they are produced simultaneously, because they are just slightly different in frequency there is an oscillation in amplitude perceived by your ear. If you were tuning a piano you would compare the sound produced by the piano to the sound produced by a tuning fork having the same note. If you noticed a beat occurring, you would know that the piano key was just a little off from the correct frequency it should be generating and you would adjust the tension in the piano string until the (beat was no longer noticeable and the note produced by the piano matched the frequency produced by the tuning fork. A properly made tuning fork always produces the correct pitch (frequency) unless it is damaged. These are precise instruments and their cost shows it. In turn, if you have the "ear" for it, you could tune a guitar off of the piano. References suggest that the human ear can detect a "beat frequency" (the difference in frequency between the two simultaneously produced frequencies) as large as 7 Hz. If the difference is larger than 7 Hz, the human ear hears a more complex (mixed frequency) wave, but does not perceive the beat pattern of oscillating amplitude.

An unpleasant sound is a mixture of tones (pitches or frequencies) called a dissonance. A dissonance is defined as an inharmonious sound or an inharmonious combination of tones produced simultaneously (discord). Dissonant is the adjective of the noun dissonance as in "a dissonant sound". A pleasant sound is called a consonance. A consonance is defined as a pleasing combination of simultaneous musical sounds (tones) or harmony of tones. Consonant is the adjective of the noun consonance as in "a consonant sound". A long time ago, in ancient Greece, Pythagorus discovered that consonant sounds are perceived when the pitches (frequencies) produced simultaneously have ratios that are that are the ratios of small whole numbers. When this happens the sound is pleasant. It is a consonant sound. The lowest frequency produced by an instrument when a note is played is called a fundamental. Waves of higher frequency produced by the instrument when a note is played are called overtones. No instrument produces a single pitch when a note is played. The sound you hear for a particular note played is the fundamental and the overtones combined. The fundamental is the loudest and that is what you tend to associate with the note. Single frequency, wave sounds can only be produced by devices like tuning forks. These waves are simple sine waves whereas the waves produced by playing a note on a musical instrument is a more complex wave form, because of the overtones combining with the fundamental.

Vocabulary: sound level, decibel, pitch, Doppler shift, closed pipe resonator, open pipe resonator, timbre, fundamental, harmonic, dissonance, consonance, octave, beat

Skills to be learned:

Solve speed of sound problems.

Solve problems involving resonance.

Solve problems involving beat notes.

*Describe how the human ear functions (optional)

Assignments:

Textbook: Read / Study / Learn Chapter 15 about sound and sound waves

WB Exercise(s): PS#15-1

Activities: TBA

Resources:

This Handout and the Overhead and Board Notes discussed in class

Textbook: Chapter 15

WB Lessons and Problem Sets

- “Sound, A Wave Phenomena”

( / Sound, A Wave Phenomenon

( / Sound, A Wave Phenomenon

( / Sound, A Wave Phenomenon

( / Sound, A Wave Phenomenon

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