Question

Q. A wall is moving with velocity u and a source of sound moves with velocity u/2 in the same direction as shown in figure. Assuming that the sound travels with the velocity 10u, the ratio of incident sound wavelength on the wall to the reflected sound wavelength by the wall is equal to :
(a) 9:11 (b) 11:9
(c) 4:5 (d) 5:4

Answer 1

answer : option (a) 9 : 11

velocity of wall = u

velocity of source of sound = u/2

velocity of sound = 10u

from Doppler's effect,

$f_1=f\left(\frac{v_{sound}-v_{wall}}{v_{sound}-v_{source}}\right)$

$f_1=f\left(\frac{10u-u}{10u-u/2}\right)$

$f_1=\frac{9f}{9.5}$......(1),

now frequency of sound after reflection,

$f_2=f_1\left(\frac{10u-u/2}{10u+u}\right)$

$f_2=\frac{9f}{9.5}\frac{9.5}{11}$

$f_2=\frac{9f}{11}$

$\frac{f_2}{f}=\frac{9}{11}$

we know, wavelength is inversely proportional to frequency

so, $\frac{\lambda}{\lambda_2}=\frac{9}{11}$

hence, ratio of incident sound wavelength to the reflected sound wavelength is 9 : 11.