Question

Two sound waves, P and Q, of speeds $350\text{m/s}$ and $410\text{m/s}$, are travelling from A to B and B to A respectively at the same time. If the wind speed is $35\text{m/s}$ in the direction of A to B, which sound will reach an observation at either of the destinations first?

• A. It depends on their frequency.
• B. Both reach at the same time.
• C. Q will reach first.
• D. P will reach first.

Answer 1

The correct option is D P will reach first.

Given,
$V_P=350\text{m/s}$
$V_Q=410\text{m/s}$
Speed of wind, $W=35\text{m/s}$
For sound wave P, the direction of wind is same as the direction of the wave.
Therefore the effective speed of sound,
$V_{P_{eff}}=V_P+W$
$V_{P_{eff}}=350+35=385\text{m/s}$
For sound wave Q, the direction of wind is opposite to the direction of the wave.
Therefore the effective speed of sound,
$V_{Q_{eff}}=V_Q-W$
$V_{Q_{eff}}=410-35=375\text{m/s}$
Wave P has more effective speed compared to wave Q. Therefore, for the same distance (between A and B), sound P will reach the destination first.