Final answer:
To solve for the observed frequencies both downwind and upwind from the lighthouse, the Doppler Effect formula is applied, accounting for the wind speed altering the effective speed of sound.
Step-by-step explanation:
The question revolves around the use of the Doppler Effect to determine the frequency of sound as heard by observers in different relative motion scenarios with respect to the sound source. When hearing the foghorn from the lighthouse, the frequency of sound perceived by a stationary observer will differ depending on whether the observer is upwind or downwind due to the wind's effect on the propagation of sound.
1. For the observer downwind from the lighthouse, the effective speed of sound increases by the wind speed. The observed frequency can be calculated using the Doppler Effect formula:
f' = f * (v + vr) / (v - vs)
Here, f' is the observed frequency, f is the source frequency (131 Hz), v is the speed of sound (typically around 343 m/s at 20°C), vr is the receiver's speed relative to the medium (0 m/s since the observer is stationary), and vs is the source's speed relative to the medium (-32.0 m/s downwind is negative since the source moves away from the observer).
2. For the observer upwind from the lighthouse, the effective speed of sound decreases due to the wind acting against sound propagation. The observed frequency is calculated similarly, but with vs being positive (32.0 m/s) because the wind is opposing the direction of the sound wave's travel toward the observer.