P109 Exam 2.1, Spring 2003

Instructions: This is an open book exam. You may look at anything you bring. Each question is worth 2 points unless indicated otherwise.

Questions 1-4 are the practical part of this exam. You will use a tube open at both ends to measure fundamental frequency and compare it to the calculated value using the speed of sound.

1. The thermometer reads a temperature of ______. Using this temperature, calculate the speed of sound in the room.

2. Calculate the fundamental frequency from f1 = v/[2(L + 2 EC)]. Make sure to write down and label all your measurements.

3. Using your experimental setup, find the experimental value for the fundamental frequency, f1.

4. Does your calculated value agree with your experimental value? Use the criteria set in class to determine your answer.

5. A tube closed at one end is placed in a room in which the speed of sound is 350 m/s. You place a speaker and a microphone at the open end of the tube. You then measure the time it takes for a single sound pulse to travel down the tube and back as 4.40 msec. What is the length of the tube?

6. Suppose you have a tube closed at one end of length 0.75m. How far, in meters, does a single sound pulse have to travel to make one complete cycle? Hint: Look at reflections of the pulse and determine what constitutes a complete cycle for the pulse traveling down the tube.

a) 0.75 m

b) 1.50 m

c) 2.25 m

d) 3.00 m

e) not enough information.

Questions 7-9 refer to a tube closed at one end with a fundamental frequency f1 = 119 Hz.

7. The tube has a resonance at 833 Hz. What is the harmonic number of this resonance?

8. If possible, draw the pressure standing wave pattern for the harmonic in question 7. If not possible, explain why not.

9. Suppose the length of this tube is 0.72 m. What is the wavelength of the harmonic in question 7? Note: You may ignore end correction considerations to the length. That is, answer the question pretending you know nothing about EC.

10. A sound signal has a frequency of 2.3 MHz. Find the period in sec.

11. Suppose a resonance for a tube with one end closed occurs at a frequency f= 360 Hz. Given the quality Q = 20, find the frequencies which give you the linewidth f.

Questions 12 and 13 belong together.

12. Suppose you have a 160 Hz sawtooth wave, whose fundamental sine wave has a peak-to-peak amplitude of 7 V. You input this sawtooth into a bandpass filter set at 1280 Hz. Will you see a non-zero output? Why?

13. What is the amplitude of the output signal in question 12? Note: This could be zero.

14. The peak-to-peak amplitude for a sound signal is increased to 7.5 V. If the change in power is 20 dB, what is the original peak-to-peak amplitude of the sound signal?

15. What is the relative power with respect to the fundamental for the 15th harmonic of a triangle wave?

16. Suppose we add together a triangle wave and a sine wave, which has the same frequency as the third harmonic of the triangle wave. The amplitude of the sine wave is roughly half that of the triangle wave. If we shift the phase of the sine wave by 180 degrees, the power spectrum of the resultant wave (triangle plus sine shifted 180 degrees)

a) will change compared to the power spectrum of the resultant wave without the 180 degree shift.

b) will stay the same compared to the power spectrum of the resultant wave without the 180 degree shift.

c) not enough information.

17. Suppose you have a 217 Hz square wave and a 217 Hz sawtooth wave, both with peak-to-peak amplitudes of 10 V. What is different about their power spectrums?

18. Consider two cases of two clear tones that are close together in frequency. In the first case the central frequency of the tone is 200 Hz and in the second 5000 Hz. Select the true statement.

a) The maximum beat frequencies are the same and the fusion frequencies are the same as well.

b) The maximum beat frequencies are different and the fusion frequencies are different as well.

c) The maximum beat frequencies are different and the fusion frequencies are the same.

d) The maximum beat frequencies are the same and the fusion frequencies are different.

19. Suppose you have two sound signals. If the speed of sound is 350 m/s and the first frequency at which destructive interference occurs is 250 Hz, calculate the path difference, d, between the two sound signals.

20. Two speakers, each producing a 400 Hz sound signal, are placed 1.6 m apart. An observer is placed 15 m away from the speaker, measured with respect to the midpoint of the speaker separation, where the central maximum is. How far left does the observer have to move to encounter the first maximum? Assume the speed of sound is 350 m/s. Note: Consider the central maximum as the zeroeth maximum, that is i = 0.

21. (4 points) Sketch the filter function (c) if the power spectrum at the vocal cords (in isolation) and the power spectrum recorded at the opening of the mouth (ie. observed power) are shown as below.

22. Label the harmonics fn on (a) and (b). Label the formants Fj on (c).

23. Suppose you have two frequencies, 567 Hz and 589 Hz. Will you hear beats? If so, what is the beat frequency?

24. In constructing the ribbon microphone, why did we use the mylar strip instead of a more solid material like a brass rod?

Extra Credit (2 points)

How does the fundamental frequency of a tube open at both ends compare with the fundamental frequency of a tube closed at one end? Explain why this relation holds theoretically, either with equations, pictures, or words. Assume all physical dimensions of the tubes, and the sound speeds are the same.