Question

A boat on a river blows a horn at a frequency of 215 Hz. A tugboat traveling the same direction at a speed twice that of the boat observes a frequency of 235 Hz. What is the speed of the boat?

Answer 1

let f = 215 Hz

f' = 235 Hz

we know, speed of sound, v = 343 m/s

let v_boat is the velocity of the boat

then velocity of tugboat, v_tugboat = 2*v_boat

use Doppler effect formula,

f' = f*(v + v_tugboat)/(v + v_boat)

f'*(v + v_boat) = f*(v + 2*v_baot)

235*(343 + v_boat) = 215*(343 + 2*v_boat)

235*343 + 235*v_boat = 215*343 + 215*2*v_boat

343*(235 - 215) = v_boat*(2*215 - 235)

==> v_boat = 343*(235 - 215)/(2*215 - 235)

= 35.2 m/s <<<<<<<<<<-----------------Answer