Waves - Doppler Effect:
A car is moving at 30 m/s towards an observer. If the car's horn emits sound at a frequency of 400 Hz, calculate the frequency of sound heard by the observer. Assume the speed of sound in air is 343 m/s.
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To calculate the frequency of sound heard by the observer, we need to consider the Doppler effect formula:
f' = ((v + v_observer) / (v + v_source)) * f_source
where:
f' = frequency heard by the observer
v_observer = velocity of the observer
v_source = velocity of the source
f_source = frequency emitted by the source
Given that the car is moving at a velocity of 30 m/s towards the observer, the velocity of the observer is 0 m/s (since they are stationary), and the frequency emitted by the car's horn is 400 Hz, we can calculate the frequency heard by the observer as follows:
f' = ((v + v_observer) / (v + v_source)) * f_source
= ((343 m/s + 0 m/s) / (343 m/s + 30 m/s)) * 400 Hz
≈ ((343 m/s) / (373 m/s)) * 400 Hz
= (0.92) * 400 Hz
≈ 369 Hz
Therefore, the frequency of the sound heard by the observer is approximately 369 Hz.
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