Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms-1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B ? (speed of sound in air = 340 ms-1) :

Question

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms-1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B ? (speed of sound in air = 340 ms-1) : (A) 2250 Hz (B) 2060 Hz (C) 2150 Hz (D) 2300 Hz

Tardigrade Admin · Accepted Answer

f =(v+v0/v-vs) f0 (v0 vs is taken ⊕ when approaching each other) 2000 = (340+(-20)/340-(-20)) f0 f0 = 2250 Hz.

2250 Hz

2060 Hz

2150 Hz

2300 Hz

f=v−vs​v+v0​​f0​(v0​&vs​ is taken ⊕ when approaching each other) 2000=340−(−20)340+(−20)​f0​ f0​=2250 Hz.

$f = \frac{v + v _{0}}{v - v _{s}} f_{0} (v_{0} & v_{s}$ is taken $\oplus$ when approaching each other)
$2000 = \frac{340 + ( - 20 )}{340 - ( - 20 )} f_{0}$
$f_{0} = 2250$ Hz.