A physics professor demonstrates the Doppler effect by tying a 700 Hz sound gene

Question

A physics professor demonstrates the Doppler effect by tying a 700 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm.

What is the difference between the highest frequency heard by a student in the classroom and the initial frequency of the sound generator?

Express your answer with the appropriate units.

What is the difference between the lowest frequency heard by a student in the classroom and the initial frequency of the sound generator?

Express your answer with the appropriate units.

Explanation / Answer

f = 700 Hz, L = 1 m ,

w = 100 rpm = 100*2*3.14/60 = 10.47 rad/s

velocity vs = L*w = 1*10.47 = 10.47 m/s

highest frequency will occur when the sound generator is headed toward the student, when it, the teacher and the student form a right angle, the teacher at the apex; lowest frequency when it is headed away.

velocity of sound in air v = 340 m/s

(a) when source approching student

from Doppler effect

fo = f(v+vo)/(v-vs)

fo = 700(340+0)/(340 -10.47)

fo = 722.24 Hz

Df = 722.24 - 700 = 22.24 Hz

(b) when source moving away from student

from Doppler effect

fo = f(v+vo)/(v+vs)

fo = 700(340+0)/(340 +10.47)

fo = 679 Hz

Df = 700 -679 = 21 Hz

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