Question

You are sailing between two banks of a lake. The wind is blowing at 12 m/sec from left to right and the boat is moving in the same direction at exactly the same speed. A siren is sounding on each bank at the same frequency of 1750 Hz. Use 343 m/s for the speed of sound.

a. On the boat, what frequency do you hear from the left siren?

Answer 1

The frequency heard from the left siren by someone on a boat moving at the same speed as the wind (12 m/s) will be lower due to the Doppler Effect, approximately 1682.64 Hz.

Step-by-step explanation:

The question is based on the Doppler Effect, a phenomenon observed when a sound source and an observer are in relative motion to each other. To calculate the frequency heard from the left siren by someone on a boat sailing in the same direction as the wind, we can use the Doppler Effect equation for a source and observer moving away from each other:

f' = f (v / (v + vs))

where

• f' is the observed frequency,
• f is the emitted frequency (1750 Hz in this case),
• v is the speed of sound (343 m/s), and
• vs is the speed of the source relative to the medium (12 m/s in this case).

Inserting the given values:

f' = 1750 Hz * (343 m/s / (343 m/s + 12 m/s))

f' ≈ 1682.64 Hz

Therefore, the frequency heard from the left siren by someone on the boat will be approximately 1682.64 Hz.