Question

A car is travelling on a straight road running along a field. A person standing at a distance of 'd' from the road. If the speed of car is 'u' and the actual frequency of its horn is '$f_0$' then the frequency heard by the observer when the car is closest to him is (the velocity of sound in air is v)

• A. $f_0$
• B. $f_0\frac{v}{c}$
• C. $f_0\left[\frac{v^2}{v^2-u^2}\right]$
• D. $f_0\left[\frac{v^2-u^2}{v^2}\right]$

Answer 1

Answer: (C)

$f_0\left[\frac{v^2}{v^2-u^2}\right]$

velocity of the source along the direction of the observer is $u\cos \theta$ ( refer diagram)

$f^{\prime }=f_0\frac{v}{v-u\cos \theta }$

From the diagram, $\cos \theta =\frac{ut}{vt}=\frac{u}{v}$

$\therefore f^{\prime }=f_0\frac{v}{v-\frac{u}{v}}=f_0\frac{v^2}{v^2-u^2}$