These problems are to help you study and will not be turned in or graded. I will discuss the answers to these questions in class. Assume that the speed of sound is 340 meters/sec or 1125 ft/sec in air. You may use either feet or meter units in these problems.   Remember that distance = rate* time  and f =1/t. Thus, d=rt and d=r/f,  f=r/d, etc. Usually  the relevant distance measure is the length of a wave, l. Most of problems 1-9 can be solved using these relationships.

1. If an adult male speaks with a fundamental frequency of 125 Hz, what is the wave length in meters (or feet)? What about for a child's voice at 300 Hz?

2. What are the descriptive parameters of a sinusoidal (pure tone) sound wave? That is, in terms of what properties can such waves differ from each other?

3. What is the frequency of a sound whose fundamental frequency has a wave .772 meters (= 2.53 ft) in length?

4. For a violin string vibrating at 235 Hz and 60 cm long, what is the wave length of the first (= fundamental), second and third harmonic in the string? What is the wave length of these harmonics in the atmosphere?

5. What is the frequency of a sound whose fundamental frequency has a wave .42 meters in length.

6. If the following sinusoids are added together, what will be the maximum possible amplitude of the sum wave if phase could be adjusted so as to maximize the amplitude.

(The equation above specifies a wave with a fundamental sinusoidal component as some arbitrary frequency f with amplitude A combined with the harmonic 4f with amplitude twice the amplitude of f.)

    If they have zero phase difference, the maximum amplitude will be close to what value as a maximum during the 1st 90 degrees of the fundamental cycle?

7. If a complex-tone in air has the fundamental frequency 250 Hz, what is its wave length? What is the wave length of its 3rd harmonic?

If the same tone were generated in water (where sound waves move about 4 times faster) what would be its wave length?

9. It has been claimed that if two waves of nearly the same frequency (but not identical) are added together, they will cause "beats". That is, the sum will change its amplitude periodically. Show how this occurs by drawing two waves that behave this way. Your drawing should be done carefully enough so the effect can be seen.

Vowel-related Problems.

10. A flagpole 15 meters long is waving in a strong wind and oscillates 3 times a second. What is the velocity of the transverse waves running along the pole?

11. If a speaker has a vocal tract length of 14.5 cm and articulates a schwa vowel (uniform tube, glottis closed),

(1) what are the first 3 resonances or formants?

(2) What is the effect on the three formants of protruding the lips by 2 cm? (3) What would be the resonant frequency of the first formant if the glottis is opened (like during a voiceless segment) and the trachea adds 22 cm to the length of the tract?

13. The vowel [i] is produced by a male with an initial F0 of 135 Hz followed by a glissando ending at 100 Hz. Which harmonic number (assuming F0 = harmonic number 1) is closest to the center of the F2-F3 combination formant at the beginning of the vowel and which one is closest at the end? (Use published formant values from a source that you cite in your answer.)

14. If a length of pipe is 7 meters (23 ft) long and is open at both ends and a standing wave is generated in the air of the pipe such that it has a single node in the middle of the pipe, what will be that resonant frequency in Hz? Be sure to draw a picture of the situation.

15. Now if this same pipe is closed at one end with a large plug, what is the lowest wavelength and frequency at which it will resonate?

16. Imagine a periodic sound source with a fundamental frequency (F0) of 200 Hz with all harmonics present and equal in amplitude. This is passed through an air-filled tube 9 in long that is (practically) closed at one end and open at the other. Carefully plot a graph (using graph paper) showing (a) an input spectrum, (b) the transfer function (you should postulate plausible transfer ratios for frequencies that are not at the resonant frequencies), and (c) a spectrum for the output. Plot these only for the region up to 1500 Hz.