Question

An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 21/12 = 1.059. With what speed must the bat fly toward the singer?

Answer 1

18.94 m/s

Step-by-step explanation:

The bat becomes the source of sound . Source is moving towards observer

apparent frequency = actual frequency x (V / V - V_s)

V is velocity of sound and V_s is velocity of source or bat.

apparent frequency / actual frequency = V / (V - V_s)

21 / 12 = 340 / (340 - V_s)

1.059(340 - V_s) = 340

340 x .059 = 1.059 V_s

V_s = 18.94 m/s

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