Question #164228

  In one of the original Doppler experiments, one tuba was played in a moving platform car at a

      frequency of 75Hz, and a second identical one was played on the same tone while at rest in the railway station. What beat frequency was heard if the train approached the station at a speed of

      10.0ms-1?


1
Expert's answer
2021-03-08T08:32:51-0500

Let's first find the frequency heard by the observer on the platform from the Doppler Shift formula:


fo=fs(vvvs),f_o=f_s(\dfrac{v}{v-v_s}),fo=75 Hz(343 ms343 ms10 ms)=77.25 Hz.f_o=75\ Hz\cdot(\dfrac{343\ \dfrac{m}{s}}{343\ \dfrac{m}{s}-10\ \dfrac{m}{s}})=77.25\ Hz.

Finally, we can find the beat frequency:


fbeat=f2f1=77.25 Hz75 Hz=2.25 Hz.f_{beat}=|f_2-f_1|=|77.25\ Hz-75\ Hz|=2.25\ Hz.

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