Question

Two cars $A$ and $B$ approaches a stationary observer from opposite sides with speed $15\text{m/s}$ and $30\text{m/s}$ respectively. Observer hears no beats. If the frequency of the horn of the car $B$ is $504\text{Hz}$, then the frequency of the horn of the car $A$ will be
$[$Take speed of sound $=330\text{m/s}]$

• A. $529\text{Hz}$
• B. $429\text{Hz}$
• C. $329\text{Hz}$
• D. $629\text{Hz}$

Answer 1

The correct option is A $529\text{Hz}$

Since, the person hears no beats, therefore, the apparent frequency heard by the observer from both cars must be the same.
$\Rightarrow f\times \frac{v}{v-v_{s_A}}=504\times \frac{v}{v-v_{s_B}}$
$\Rightarrow f\times \frac{330}{330-15}=504\times \frac{330}{330-30}$
$\Rightarrow f\approx 529\text{Hz}$
$$\begin{array}{c}\text{Why this question?}\\ \text{Tips: The apparent frequency heard is different than original frequency due to Doppler's effect}\\ \text{Beat frequency,}{F}_b=|f_1-f_2|\\ \text{For no beats heard,}{f}_1=f_2\end{array}$$