A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ms-1, (Given speed of sound = 300 m/s)

Question

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ms-1, (Given speed of sound = 300 m/s) (A) 16, 14 (B) 12, 18 (C) 12, 16 (D) 8, 18

Tardigrade Admin · Accepted Answer

f =480 = (300 -v1/300) ×500 (1440/5) = 300 - v1 v1 = (60/5) = 12m /s 530 = (300+v2/300) ×500 1590 = 1500 + 5v2 5v2 = 90 v2 = 18 m/s

Q. A stationary source emits sound waves of frequency $500 Hz$ . Two observers moving along a line passing through the source detect sound to be of frequencies $480 Hz$ and $530 Hz$ .
Their respective speeds are, in $m s^{- 1}$ ,
(Given speed of sound = $300 m / s$ )

16, 14

12, 18

12, 16

8, 18

$f = 480 = \frac{300 - v _{1}}{300} \times 500$
$\frac{1440}{5} = 300 - v_{1}$
$v_{1} = \frac{60}{5} = 12 m / s$
$530 = \frac{300 + v _{2}}{300} \times 500$
$1590 = 1500 + 5 v_{2}$
$5 v_{2} = 90$
$v_{2} = 18 m / s$

Q. A stationary source emits sound waves of frequency 500Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480Hz and 530Hz. Their respective speeds are, in ms−1, (Given speed of sound = 300m/s)