Question

Two cars moving in opposite directions approach each other with a speed of $22\text{m/s}$ and $16.5\text{m/s}$ respectively. The driver of the first car blows a horn having a frequency $400\text{Hz}$. The frequency heard by the driver of the second car is [velocity of sound is $340\text{m/s}]$

[Assume, medium is stationary ]

• A. $350\text{Hz}$
• B. $361\text{Hz}$
• C. $411\text{Hz}$
• D. $448\text{Hz}$

Answer 1

The correct option is D $448\text{Hz}$

Given,
Velocity of source $\left(v_s\right)=22\text{m/s}$

Velocity of observer $\left(v_o\right)=16.5\text{m/s}$

Velocity of sound in the stationary medium $\left(v\right)=340\text{m/s}$

Original frequency of sound $\left(f_0\right)=400\text{Hz}$

When source and observer are moving towards each other, then the apparent frequency heard by the observer is given by

$f_{app}=f_0\left[\frac{v+v_o}{v-v_s}\right]$

Substituting the given data,

$f_{app}=400\left[\frac{340+16.5}{340-22}\right]=448\text{Hz}$.