A boy riding on his bike is going towards east at a speed of  $4\sqrt{2}\text{\hspace{0.17em}m}/\text{s}$. At a certain point, he produces a sound pulse of frequency $1650\text{\hspace{0.17em}Hz}$ that travels in air at a speed of $334\text{\hspace{0.17em}m}/\text{s}$ . A second boy stands on the ground  ${45}^0$ south of east from him. The frequency of the pulse as received by the second boy is (in $\text{Hz}$)

1. Speed of boy  $v=4\sqrt{2}\text{\hspace{0.17em}m}/\text{s}$
Frequency of sound pulse  $v_0=1650\text{\hspace{0.17em}Hz}$
$B_1$ or the first boy is the source of the sound and  $B_2$ is the listener. $v_s$  is the component of the velocity of the source along the source – listener axis (SL axis). Here,
$v_s=4\sqrt{2}\cos {45}^0=4\text{\hspace{0.17em}m}/\text{s}$ 

 
Using Doppler’s effect formula  $v=\left(\frac{v-v_L}{v-v_A}\right)v_0$
Speed of sound in air
$v=334\text{\hspace{0.17em}m}/\text{s},v_s=4\text{\hspace{0.17em}m}/\text{s},v_L=0$ 

$v=\left(\frac{334}{334-4}\right)\times 1650\text{\hspace{0.17em}Hz}=\frac{334}{330}\times 1650\text{\hspace{0.17em}Hz}=1670\text{\hspace{0.17em}Hz}$
Therefore, the correct answer is 1670.00