Practice

 

  1. Explain how you could determine if a speaker was male or female by inspecting the sound spectrum of a spoken vowel. (frequency of format)
  2. Why does the pitch of your voice go up when you inhale Helium? (speed of sound is higher in Helium so f = v/lλ)
  3. Suppose a vocal tract 17 cm long is filled with Helium (Vsound = 970 m/s). Where would you expect the main resonances of the trachea to be in this case?(f1 = v/4L = 1400 Hz, f3 = 4200 Hz, f5 = 7000 Hz etc)
  4. A piano tuner finds that two strings tuned to C4 produce one beat per second when sounded together. What is the ratio of their frequencies and by how many cents do their pitches differ? (1.0038, 6.6c)
  5. In building a glockenspiel a musician chose an aluminum bar 21.4 cm long and 9 mm thick. Sketch the first two transverse modes and identify the nearest notes that these modes produce. (1031.4 Hz, 2843.9 Hz, C6, F7. used v = 5100 m/s)
  6. Find the first three modes of a 0.75 m pipe open one-end. Assume Vsound = 350 m/s. Are these modes harmonics? (ignore end correction if diameter not given so f1 = 1116.7, f3 = 350 , f5 = 583.3 Hz)
  7. Are overtones and harmonics just different names for the same thing? Explain.
  8. Human hearing is most sensitive around 4000 Hz - Explain how this allows you to estimate the size of the ear canal?
  9. If two sounds differ by 43 dB what is the ratio of their sound intensities?(19952.6)
  10. At what point would you divide a 65 cm long guitar string to produce two notes an octave apart? How about a perfect third? (21.7 cm from one end, the seconfd part is too ambiguous - if I use a Just Intonation then ratio is 5/4 so divide string at 28.9 cm from one end)
  11. Two square waves of 200 and 301 Hz are sounded together. How many beats are heard? Explain this by writing out the first 5 harmonics of each tone.(remember that a square wave only has odd harmonics, modes are 200, 600, 1000, 1400, 1800 HZ and 301, 903, 1505, 2107 etc - if you do hear a bat it will be around 101 Hz - the situation would be quite different, however, if all harmincs were present)
  12. In an equally tempered system what frequency is a fifth above 401Hz? (a 5th is 700c above in the tempered system so f = 600.8 Hz)
  13. Why are the overtones in a piano not purely harmonic? (strings are not 1D but are vibrating columns - so inharmonicity!)
  14. An guitar is tuned to be within 1% of A440 - is this good enough? How many cents sharp or flat will it be?(NOT VERY GOOD! - about 17c off)
  15. A young girl is practicing her clarinet in the family car on the way home from school. She plays an E4 as she approaches you at a speed of 20 m/s. Do you hear a sharp or flat E4 (provide a quantitative answer please).(you hear f = 350 Hz, sharp close to F4 - I used Vsound = 343 m/s)