Question

Iron man loves to listen to the Doppler Effect. While waiting for a commuter train that blows its 200-Hz horn as it approaches a crossing he observes the frequency to be 208 Hz. [It is a nice day and the speed of sound is 335 m/s] What frequency does he observe as the train moves away?

Answer 1

192.6 Hz

Step-by-step explanation:

v = Velocity of sound in air = 335 m/s

Actual frequency = 200 Hz = f

Observed frequency = 208 Hz =
`f_o`

Speed of train =
`v_t`

Doppler effect when the source is moving towards observer

`f_o=(v)/(v-v_t)f\\\Rightarrow 208 = (335)/(335-v_t) 200 \\\Rightarrow 335-v_t = (335* 200)/(208)\\\Rightarrow 335-v_t=322.11\\\Rightarrow v_t = 12.88\ m/s`

Doppler effect when the source is moving away from observer

`f_o=(v)/(v+v_t)f\\\Rightarrow f_o=(335)/(335+12.88)200\\\Rightarrow f_o=192.6\ Hz`

∴ Frequency he observes as the train moves away is 192.6 Hz