Question

A source of sound emits waves of frequency $f_0=1200\text{Hz}.$ The source is travelling with a velocity $v_1=30\text{m/s}.$ towards east. There is a large reflecting surface in front of the source which is travelling with a velocity $v_2=60\text{m/s}$ towards west. Speed of sound in air is $v=330\text{m/s}$. Find the ratio of wavelength $\left({\lambda }_1\right)$ of sound emitted by source when travelling towards the reflecting surface to the wavelength $\left({\lambda }_2\right)$ of sound approaching the source after getting reflected.

• A. $\frac{9}{13}$
• B. $\frac{7}{15}$
• C. $\frac{13}{9}$
• D. $\frac{15}{7}$

Answer 1

The correct option is C $\frac{13}{9}$

Frequency received by the reflector is

$f=f_0\left[\frac{v+v_2}{v-v_1}\right]$

From the data given in the question,

$f=1200\left[\frac{330+60}{330-30}\right]=1200\times \frac{390}{300}=1560\text{Hz}$

Before reflection, wavelength of wave emitted by source

${\lambda }_1=\frac{v-v_1}{f_0}=\frac{330-30}{1200}=\frac{1}{4}\text{m}$

After reflection, wavelength of wave emitted by reflecting surface

${\lambda }_2=\frac{v-v_2}{f}=\frac{330-60}{1560}=\frac{27}{156}=\frac{9}{52}\text{m}$

$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{4}\times \frac{52}{9}=\frac{13}{9}$