Question

A car approaching a crossing at a speed of $50\text{m/s}$ blows a horn of frequency $500\text{Hz}$ when $30\text{m}$ away from the crossing. The speed of sound in air is $330\text{m/s}$. What frequency will be heard by an observer at rest at $40\text{m}$ from the crossing?

• A. $540\text{Hz}$
• B. $550\text{Hz}$
• C. $560\text{Hz}$
• D. $570\text{Hz}$

Answer 1

The correct option is B $550\text{Hz}$

Pictorially we can depict the problem as shown below.

The frequency heard by observer,
$f^{{}^{\prime }}=f_0\left(\frac{v+v_0}{v-v_s}\right)$, where $f_0=500\text{Hz},v_0=0\text{m/s},v=330\text{m/s}\text{and}{v}_s=50\text{m/s}$
$\Rightarrow f^{{}^{\prime }}=f_0\left(\frac{v+v_0}{v-v_s\cos \theta }\right)$
[we take speed of source and observer along line joining the source and observer]
$\Rightarrow f^{{}^{\prime }}=500\times \left(\frac{330+0}{330-50\times \frac{30}{50}}\right)$
$\Rightarrow f^{{}^{\prime }}=550\text{Hz}$