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?
The speed of the bat is 9.74 m/s
The frequency ratio of two notes is 21/12 = 1.059
The speed of the sound is vs = 340 m/s
Let the speed of the bat is vb
The frequency reflected by the bat is given by
Here, f= frequency of the sound source
vs = speed of the soundvb= speed of the bat
According to the statement given,
Substitute the known values,
Thus, the speed of the bat is 9.74 m/s
You are standing at x = 0 m, listening to a sound that is emitted at frequency . The graph of FIGURE Q16.12 shows the frequency you hear during a 4-second interval. Which of the following describes the sound source? Explain your choice.
A. It moves from left to right and passes you at t = 2 s.
B. It moves from right to left and passes you at t = 2 s.
C. It moves toward you but doesn’t reach you. It then reverses direction at t = 2 s.
D. It moves away from you until t = 2 s. It then reverses direction and moves toward you but doesn’t reach you
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