Question

 A train is moving parallel and adjacent to a highway with a constant speed of 32 m/s. A car is traveling in the same direction as the train at 64 m/s. The car's horn sounds at 520 Hz and the train's whistle sounds at 320 Hz.

 When the car is behind the train what frequency does an occupant of the car observe for the train whistle? The speed of sound is 343 m/s.

 Answer in units of Hz.

 When the car is in front of the train what frequency does a train passenger observe for the car's horn?

 Answer in units of Hz.

Answer 1

The Doppler effect for the moving train is,

The frequency of the observer f¹¹=520HZ

The frequency of the source is f¹=320HZ

velocity of the source is v+=32m/s

velocity of the observer is v-=64m/s

Then, f¹¹=f¹(v+/-v₀)/(v-/v_s)

   520=320(32/-v₀)/(64/v_s)

-v_s/v₀=3.25m/s

But we want to the observer frequency of the car observing train whistle frequency is,

f¹¹=f¹(v+/-vo)/(v-/+vs)

=320(-32/343)(3.25)

=97HZ

so the frequency of the train whistle observed by the car is 97HZ