Question

A horn is rotated in circle of radius 1 m. Its frequency is 500 Hz. The maximum and minimum frequencies heard by a man near the horn outside the circle are in the ratio 101/99. The velocity of horn is..
1) 34 m/sec
2) 340 m/sec
3) 0.34 m/sec
4) 3.4 m/sec

Answer 1

Given:

source frequency(f0) = 500 Hz

radius = 1m

max frequency/min frequency = 101/99

To Find:

the velocity of horn =?

Solution:

now, from the doppler effect, we know that

f max =  $f0 \times \dfrac{v}{v-u}$

here v = speed of sound in medium (assume its air) = 330m/s (we know that)

now lly,

 $f min =f0 \times \dfrac{v}{v+u}$

now given, max frequency/min frequency = 101/99

putting values in above equation

$\dfrac{110}{99} = \dfrac{v+u}{v-u}$

on putting value of v and solving for u we get

u = 3.4 m/s

Thus, the velocity of horn is 3.4m/s ( option4 )