Samira is riding on a bus moving at 14 m/s when she hears a whistle on the road ahead of her. If the bus is moving towards the whistle and the whistle emits a 2400 Hz sound, what frequency sound does Samira hear? You can assume that the whistle is not moving and that the speed of sound in air is 350 m/s.2496 Hz2400 Hz 2154 Hz2304 Hz
Question
Samira is riding on a bus moving at 14 m/s when she hears a whistle on the road ahead of her. If the bus is moving towards the whistle and the whistle emits a 2400 Hz sound, what frequency sound does Samira hear? You can assume that the whistle is not moving and that the speed of sound in air is 350 m/s.2496 Hz2400 Hz 2154 Hz2304 Hz
Solution
To solve this problem, we need to use the Doppler effect formula for sound. The Doppler effect describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source.
The formula for the observed frequency when the source is stationary and the observer is moving towards the source is given by:
where:
- is the observed frequency,
- is the emitted frequency (2400 Hz),
- is the speed of sound in air (350 m/s),
- is the speed of the observer (14 m/s).
Now, let's plug in the values:
First, calculate the numerator:
Next, divide by the speed of sound:
Now, multiply by the emitted frequency:
So, the frequency sound that Samira hears is approximately 2496 Hz.
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