A car moving at 16.0 m/s, passes an observer while its horn is pressed. Find the difference between the frequencies of sound heard when the car approaches and when it recedes from the stationary observer. The velocity of sound is 343 m/s and the frequency of the sound of the car's horn is 583 Hz.
same for the next 2
I got 61.8 Hz
To find the difference between the frequencies of sound heard when the car approaches and when it recedes from the stationary observer, we need to use the formula for the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by someone moving relative to the source of the wave.
The formula to calculate the observed frequency of a moving sound source is:
f' = ((v + vo) / (v - vs)) * f
Where:
- f' is the observed frequency
- v is the velocity of sound (343 m/s)
- vo is the velocity of the observer (0 m/s since the observer is stationary)
- vs is the velocity of the source (in our case, the velocity of the car)
- f is the frequency of the sound source (583 Hz)
Let's calculate the observed frequency when the car approaches the observer:
f'approach = ((v + vo) / (v - vs)) * f
= ((343 + 0) / (343 - 16)) * 583
= (343 / 327) * 583
= 611.32 Hz (approximately)
Now, let's calculate the observed frequency when the car recedes from the observer:
f'recede = ((v + vo) / (v + vs)) * f
= ((343 + 0) / (343 + 16)) * 583
= (343 / 359) * 583
= 557.63 Hz (approximately)
The difference between the frequencies is:
Difference = f'approach - f'recede
= 611.32 Hz - 557.63 Hz
= 53.69 Hz (approximately)
Therefore, the difference between the frequencies of sound heard when the car approaches and when it recedes from the stationary observer is approximately 53.69 Hz, not 61.8 Hz as you mentioned.