Question

Two trains, each moving with a velocity of $30m/s$, cross each other. One of the trains gives a whistle whose frequency is $600Hz$. If the speed of sound is $330m/s$, the apparent frequency for passengers sitting in the other train before crossing would be:

• A. $600Hz$
• B. $630Hz$
• C. $920Hz$
• D. $720Hz$

Answer 1

The correct option is D

$720Hz$

Step 1: Given

Velocity of source (the train that whistles): $v_s=30m/s$

Velocity of observer (the people in other train): $v_o=-30m/s$ (negative, because going in different direction)

Frequency of whistle: $f=600Hz$

Speed of sound: $v=330m/s$

The apparent frequency for passenger $f\text{'}$

Step 2: Formula Used

$f\text{'}=f\left(\frac{v-v_o}{v-v_s}\right)$

Step 3: Calculate the apparent frequency using the formula

$$\begin{gathered} f\text{'}=600\left(\frac{330-\left(-30\right)}{330-30}\right) \\ =600\left(\frac{360}{300}\right) \\ =600\times \frac{6}{5} \\ =720Hz \end{gathered}$$

Hence, the apparent frequency for passengers is $720Hz$. Option D is correct.