Answer to Question #164228 in Optics for Ulrich

Question

  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?

Answer 1

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

$$f_o=f_s(\dfrac{v}{v-v_s}),$$ $$f_o=75\ Hz\cdot(\dfrac{343\ \dfrac{m}{s}}{343\ \dfrac{m}{s}-10\ \dfrac{m}{s}})=77.25\ Hz.$$

Finally, we can find the beat frequency:

$$f_{beat}=|f_2-f_1|=|77.25\ Hz-75\ Hz|=2.25\ Hz.$$