MidTerm2Sol

# MidTerm2Sol - PHY 126-07 Mid-term Exam II Chapters...

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Chapters 15,16,17,18 Problem 1 (10+10 points) A scientist is making a mockup model of a human ear using a small can with the top surface open and the bottom closed. A human ear is especially sensitive to sound whose frequency is 3,440 Hz. If this is the lowest frequency that the ear is especially sensitive to, (a) what the height of the mockup model h should be? Assume that the speed of sound is 344 m/s. (b) What is the next lowest frequency the ear especially sensitive to? open closed Solution : (a) This is an example of standing waves in a stopped pipe. When the incoming sound wave’s frequency coincides with or is very close to the frequencies of standing waves the ear is especially sensitive to the sound as resonance occurs (4 points). Therefore the fundamental frequency f 1 =v/(4h) where v is the speed of sound (3 points). From 3440 s -1 = (344 m/s)/(4h), h=1.00/40.0= 0.025 m (3 points). (b) The n-th harmonic frequency is described by: f n =nv/(4h) where n=1,3,5,…(odd integer) (5 points). A harmonics with an even integer n does not exist. Therefore the next lowest frequency is when n=3. f 3 =3v/(4h)=3(344 m/s)/(4 x 0.025 m) = 10,300 Hz (5 points). h

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MidTerm2Sol - PHY 126-07 Mid-term Exam II Chapters...

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