Question

Two bikes moving in opposite directions approach each other with speed of $40\text{m/s}$ and $20\text{m/s}$ respectively. The first bike sounds a horn having a frequency $380\text{Hz}$. The frequency heard by the biker of the second bike is
[velocity of sound in air is $340\text{m/s}]$

• A. $450\text{Hz}$
• B. $460\text{Hz}$
• C. $465\text{Hz}$
• D. $456\text{Hz}$

Answer 1

The correct option is D $456\text{Hz}$

From Doppler effect,
Apparent frequency, $f_{app}=f_0\left[\frac{v+v_0}{v-v_s}\right]$
where
$f_0$ = original frequency blown by the source $=380\text{Hz}$
Velocity of sound in air $v=340\text{m/s}$
$v_0$ = velocity of observer $\left(2^{nd}\text{biker}\right)=20\text{m/s}$
$v_s$ = velocity of source $\left(1^{st}\text{biker}\right)=40\text{m/s}$
Frequency heard by the biker of second bike.
$f_{app}=380\left(\frac{340+20}{340-40}\right)=\frac{380\times 360}{300}=456\text{Hz}$