Question

A boy riding on his bike is going towards west at a speed of $6\text{m/s}$. At a certain point, he produces a sound pulse of frequency $1005\text{Hz}$, that travels in air at a speed of $338\text{m/s}$. A second boy stands on the ground ${60}^{\circ }$ south of west from him. Find the frequency of the pulse as received by the second boy.

• A. $1005\text{Hz}$
• B. $1050\text{Hz}$
• C. $1014\text{Hz}$
• D. $1100\text{Hz}$

Answer 1

The correct option is C $1014\text{Hz}$

Given that
Speed of bike or source $\left(v_s\right)=6\text{m/s}$
Speed of sound $\left(v\right)=338\text{m/s}$
Actual frequency $\left(f_0\right)=1005\text{Hz}$


From the definition of Doppler effect,

$f_{app}=f_0\left(\frac{v\pm v_o}{v\pm v_s}\right)$
Here, velocity of observer
$v_o=0\text{m/s}$ and
velocity of source along line joining source and observer
$v_s^{\prime }=v_s\cos \theta =6\cos {60}^{\circ }=3\text{m/s}$

$\Rightarrow f_{app}=f_0\left(\frac{v}{v-v_s^{\prime }}\right)$
Substituting the given data,
$f_{app}=1005\left(\frac{338}{338-3}\right)=1014\text{Hz}$