Pre-Lab: Electric Fields



Pre-Lab: Resonance of an Air Column Name:

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Choose the best answer. (20 pts total)

1. What are we trying to determine in this lab when we observe the resonance of sound waves in an air column? [1 pt]

a. the frequency of the sound waves c. the temperature of the air

b. the volume of the sound waves d. the speed of sound in air

2. Write a formula for the speed of any wave in terms of frequency and wavelength. [1 pt]

3. The lab apparatus is a tube. Is it …? [1 pt]

a. closed at both ends

b. open at one end and closed at the other

c. open at both ends

4. In a tube with both ends open, the position (length of tube) of the first resonance occurs at

a. (/4 b. (/2 c. 3(/4 d. ( [1 pt]

5. The position of the second resonance occurs another _____ after the first resonance (tube open both ends). [1 pt]

a. (/4 b. (/2 c. 3(/4 d. (

6. Sketch in the wavelength for the first resonance in a double open ended tube as in Figure 1 of your lab manual. [1 pt]

[pic]

7. Compare equation 2 and the algebraic equation of a straight line to find what the slope of a graph of wavelength versus the inverse of frequency is equal to. [1 pt]

“y” = slope “x” + y-intercept slope =

8. What are the (SI) units of the slope of a plot wavelength vs. the inverse of frequency? [1 pt]

a. m/s b. s/m c. Hz d. m/s2

9. What is the “inverse of frequency” equal to? [1 pt]

a. period b. Hertz c. speed of sound d. wavelength

10. In the empirical equation for the speed of sound from the lab manual (equation 3), what units must Tc be? [1 pt]

a. m/s b. °C c. K d. s

11. The adjacent table contains some data from the Resonance of an Air Column Lab (tube open at both ends. Fill in the blanks in the table. [3 pts]

|Antinode positions |285 Hz |375 Hz |490 Hz |

|x1 (cm) |29.3 |0.3 |13.8 |

|x2 (cm) |89.5 |46.2 |49.1 |

|x3 (cm) |-------------- |91.5 |83.9 |

|average difference in antinode |60.2 | |35.05 |

|positions, | | | |

|xave internodal (cm) | | | |

|( (cm) |120.4 | |70.1 |

|1/f (sec) |0.00351 |0.00267 | |

12. A graph of λ vs. 1/f (wavelength versus inverse of frequency) was made based on the data in the above table. A best fit straight line was drawn and two easy to read points on the line were chosen: (x1, y1) = (0.00248 s, 0.86 m); (x2, y2) = (0.00356 s, 1.22 m). Use these points to calculate the slope of the line (and the speed of sound in the air when the data was taken). [1 pt]

a. 333 m/s b. 0.00300 m/s c. 1926 m/s d. 343 m/s e. 347 m/s

Note: The diagrams below show a cartoon of the lab apparatus positioned at different lengths. The inner tube has a scale mounted on it and slides in and out of the outer tube. The apparatus can produce tube lengths between approximately 0.9 m and 1.8 m. The gray outer tube is ~90.0 cm

[pic] [pic]

13. Given a speed of sound in the air of v = 345 m/s (this depends on air temperature) and a tuning fork frequency of 320 Hz, determine the expected resonant points on the lab apparatus. You will be doing this in the lab (step 8). Follow the steps below. Show your work. [6 pts total]

First: Use the speed of sound and the frequency of the tuning fork to calculate the wavelength.

λ = v/f = (1 pt)

Second: Calculate the lengths, Ln, of the tube for the first four resonant positions. (See pg 3 of lab)

L1 = (1) λ/2 = (1) (1.078 m)/2 = 0.539 m = 53.9 cm (2 pts)

L2 = (2) λ/2 = (2) (1.078 m)/2 = 1.078 m = 107.8 cm

L3 =

L4 =

Third: Which Ln can be seen on our lab apparatus? (Allowable tube lengths ~90-180 cm)? (1 pt)

Can be seen: L2 & ______ Cannot be seen: L1 & _____

Fourth: Calculate the relative position on the inner pipe scale (outer pipe is ~90 cm long) (2 pts)

For L1: dp1 = 53.9 cm – 90 cm = -36.1 cm (lab apparatus is too short)

For L2: dp2 = 107.8 cm – 90 cm = 17.8 cm (resonance expected at 17.8 cm on inner tube)

For L3: dp3 =

For L4: dp4 =

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