Question

A train moving at a speed of $20 \, m \, s^{- 1}$ towards a stationary object emits a sound of frequency $930 \, Hz$ . Some part of the wave gets reflected from the object, back to the train as an echo. The frequency of this echo, as detected by the driver of the train is [speed of sound in air is $330 \, m \, s^{- 1}$ ]

• A. $1400Hz$
• B. $1750Hz$
• C. $1050Hz$
• D. $1550Hz$

Answer 1

Answer: (C)

The speed of the train, $v_{\text{T}}=\text{20 m s}^{-1}$
The speed of sound in air, $v=\text{330 m s}^{-1}$
The frequency of the echo detected by the driver of the train is
$v'=v\left(\frac{v + v_{T}}{v - v_{T}}\right)$
$v'=930\left(\frac{330 + 20}{330 - 20}\right)=930\times \frac{350}{310}Hz$
$\Rightarrow v'=1050Hz$