You're in an auto traveling at 25.0m/s toward a pole mounted warning siren. If the siren's frequency is 365 Hz, what frequency do you hear? Use 343m/s as the speed of sound.
nwueid
To determine the frequency you hear, you need to consider the Doppler Effect. The Doppler Effect describes how the perceived frequency of a sound wave changes when there is relative motion between the source of the sound wave and the observer.
In this case, you are the observer and the pole-mounted warning siren is the source of the sound wave. The Doppler Effect equation for sound waves is given by:
f = (v + vo) / (v + vs) * fs
Where:
- f is the observed frequency (the frequency you hear)
- v is the speed of sound in the medium (343 m/s in this case)
- vo is the velocity of the observer (the velocity of your auto)
- vs is the velocity of the source (the velocity of the pole-mounted warning siren)
- fs is the frequency of the source (365 Hz in this case)
In this scenario, you are traveling toward the pole-mounted warning siren, so your velocity (vo) is positive. However, the velocity of the source (vs) is stationary, so it is 0.
Plugging in the values into the equation, we get:
f = (343 + 25) / (343 + 0) * 365
f = 368 / 343 * 365
f ≈ 393.18 Hz
Therefore, you would hear a frequency of approximately 393.18 Hz.