Question

A train standing at a signal of a railway station blows a whistle of frequency 256 Hz in air. Calculate the frequency of the sound as heard by a person standing on the platform when the train i) approaches the platform with a speed of 40m/s ii) recedes from the platform with the same speed.speed of sound in air = 340m/s

Answer 1

$$\begin{gathered} actualfrequency{\nu }_0=256HZ \\ 1)Apparentfrequencyisgivenby: \\ \nu =\frac{v}{v-v_s}{\nu }_0 \\ wherevisthevelocityofsound \\ {v}_s=velocityoftrain \\ \nu =\frac{340}{340-40}\times 256=290.13Hz \\ 2)\nu =\frac{340}{340+40}\times 256=229.05Hz \end{gathered}$$