JEE PYQ: Waves And Sound Question 29
Question 29 - 2019 (10 Apr Shift 1)
A stationary source emits sounds 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)
(1) 12, 16
(2) 12, 18
(3) 16, 14
(4) 8, 18
Show Answer
Answer: (2)
Solution
Frequency of sound source ($f_0$) = 500 Hz
When observer is moving away from the source:
Apparent frequency $f_1 = 480 = f_0\left(\frac{v - v_0}{v}\right)$ …(i)
And when observer is moving towards the source:
$f_2 = 530 = f_0\left(\frac{v + v_0}{v}\right)$ …(ii)
From equation (i): $480 = 500\left(\frac{300 - v_0}{300}\right)$
$v_0 = 12$ m/s
From equation (ii): $530 = 500\left(\frac{300 + V_0’}{300}\right)$
$\therefore V_0’ = 18$ m/s
BETA
