Question

Two cars $A$ and $B$ both are moving towards each other with a speed of $7.2\text{km/hr}$. Car $A$ produces a sound of frequency $676\text{Hz}$. Find the beat frequency (Hz) heard by the person sitting in car $A$.
[Speed of sound is $340\text{m/s}$ in air]

• A. $16$
• B. $12$
• C. $18$
• D. $14$

Answer 1

The correct option is A $16$

Given that,
Speed of car $A$ and $B,v=7.2\text{km/h}=2\text{m/s}$
Frequency observed by person in Car $A$ of sound directly received, $f_1=676\text{Hz}$
Now, frequency of sound received by person in Car $B$,
$f=\left(\frac{v+v_o}{v-v_s}\right)\times f_1=\left(\frac{340+2}{340-2}\right)\times 676$
$=684\text{Hz}$
Further,
Frequency of sound observed by person in Car $A$ of sound received after reflection from Car $B$,
$f_2=\left(\frac{v+v_o}{v-v_s}\right)\times f=\left(\frac{340+2}{340-2}\right)\times 684=692\text{Hz}$
Therefore, beat frequency, $f_B=f_2-f_1$
$\Rightarrow f_B=692-676$
$\Rightarrow f_B=16\text{Hz}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Concept - When separation between the source and}\\ \text{observer decreases, then the apparent frequency}\\ \text{increases and vice-versa.}\end{array}$