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Question:

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

12,16

12,18

8,18

16,14

Solution:

The correct option is B (12,18)

For the observer detecting 480 Hz:
480 = 300 - v1 / 300 * 500
14400 = 150000 - 500v1
500v1 = 6000
v1 = 12 m/s

For the observer detecting 530 Hz:
530 = 300 + v2 / 300 * 500
159000 = 150000 + 500v2
500v2 = 9000
v2 = 18 m/s