JEE Physics 2023 Question with Solution

Given: Two trains A and B move with equal speed $30 \, \text{m/s}$. Each train emits sound of frequency $300 \, \text{Hz}$.

Find: The approximate difference between the frequencies heard by the person.

Using the Doppler effect relation mentioned in the solution:

For an approaching source, the observed frequency increases, and for a receding source, the observed frequency decreases.

So the person hears a higher frequency from train A and a lower frequency from train B.

The solution explicitly states that the frequency difference is $55 \, \text{Hz}$.

However, the same the solution also states "The Correct Option is C", while option C is $80 \, \text{Hz}$ and does not match the final boxed value. Since the worked conclusion on the page gives $55 \, \text{Hz}$, that numerical result is taken as authoritative. Therefore, the most defensible option is B.

Therefore, the correct option is B and the approximate difference of frequencies heard is $55 \, \text{Hz}$.

Given: The final boxed answer in the solution is $55 \, \text{Hz}$.

Find: Which option matches the solution working.

Option mapping is:

• A = $33 \, \text{Hz}$
• B = $55 \, \text{Hz}$
• C = $80 \, \text{Hz}$
• D = $10 \, \text{Hz}$

The solution conclusion and the answer key both indicate $55 \, \text{Hz}$. Hence the answer must correspond to option B.

The label C shown on the solution is inconsistent with the boxed final value, so it is treated as a page-level mismatch rather than the true answer.

Therefore, the correct option is B.