Question

A highway truck has two horns $A$ and $B$. When sounded together, the driver records $50$ beats in $10$ seconds. With horn $B$ blowing and the truck moving towards a wall at a speed of $10 \,m / s$, the driver noticed a beat frequency of $5 \,Hz$ with the echo. When frequency of $A$ is decreased the beat frequency with two horns sounded together increases. Calculate the frequency of horn $A$. $($ Speed of sound in air $=330\, m / s )$

• A. 75 HZ
• B. 85 Hz
• C. 90 HZ
• D. 95 Hz

Answer 1

Answer: (A)

Here, let frequencies of horn $A$ and $B$ are $n_{A}$ and $n_{B}$, respectively.
As given, $n_{A}-n_{B}=\frac{50}{10}$
$n_{A}-n_{B}=5 $ beats
When, the horn $B$ is blown while moving towards the wall the apparent frequency,
$n_{B}^{'}=n_{B} \frac{v+v_{0}}{v-v_{s}}$
Since, both the observer and source are moving with truck.
So $v_{s} =v_{0}=10\, m / s $
$n_{B}^{'} =n_{B}\left(\frac{330+10}{330-10}\right) $
$n_{B}^{' } =n_{B} 1.0625$
$= n_{B}{ }^{'}-n_{B}=0.0625\, n_{B}$
As given, $n_{B}^{'} -n_{B} =5 $
$0.0625 \,n_{B} =5$
$n_{B} =80 \,Hz$
$\because$ Given, that if frequency of $A$ is decreased then beat frequency is increases.
So, $ n_{B} > n_{A} $
$ \therefore n_{A}=n_{B}-5=80-5 $
$\Rightarrow n_{A}=75\, Hz $