One piano is at rest,and another one approaches at 3.4 m/s.Both pianists are playing middle C (512 Hz).What beats does the pianist at rest hear as a result of the Doppler shift? (Use 340 m/s for v_sound.) A)10 B)20 C)5 D)512 E)no beats

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Quizplus · Accepted Answer

When the piano at rest hears the approaching piano play middle C, it will perceive a Doppler shift in frequency due to the motion of the second piano. The formula for the observed frequency is given by f' = f ((v + vS1U1B0)/(v + vS2U2B0)), where f is the emitted frequency, v is the relative velocity between the two pianos, and vS1U1B1soundS1U1B0 is the speed of sound. Plug in the values given: f' = 512 ((3.4 + 0)/(3.4 + 340)) = 505.94 Hz. The frequency difference between the two pianos is 512-505.94 = 6.06 Hz. Since 6.06 is close to 5, the closest option is (C), 5 beats. Thus, the pianist at rest hears 5 beats due to the Doppler shift.

One Piano Is at Rest,and Another One Approaches at 3