A baseball hits a car, breaking its window and triggering its alarm which sounds at a frequency of 1250 Hz. What frequency (in Hz) is heard by a boy on a bicycle riding away from the car at 6.50 m/s? Take the speed of sound to be 343 m/s.
source at rest, observer moving away.
f= (343-6.50)/343 * 1250
1226.3
To calculate the frequency heard by the boy on the bicycle, we need to take into account the Doppler effect. The Doppler effect occurs when there is relative motion between the source of sound (the car) and the observer (the boy on the bicycle).
The formula for the observed frequency (f') due to the Doppler effect is:
f' = f * (v + v₀) / (v + vs)
Where:
- f is the frequency of the source (1250 Hz, in this case).
- v is the speed of sound (343 m/s).
- v₀ is the speed of the observer towards the source, which is 0 since the boy is moving away from the car.
- vs is the speed of the source towards the observer, which is the speed of the car (unknown).
We can rearrange the formula to solve for vs:
f' * (v + vs) = f * v
vs = (f * v - f' * v) / f'
Substituting the given values:
f = 1250 Hz
v = 343 m/s
v₀ = 0 m/s
f' = ?
To find f', we need to take into account the effect of the observer moving away from the car. When an observer moves away from a stationary source of sound, the observed frequency decreases.
The formula to calculate the observed frequency due to the relative motion of the observer is:
f' = f * (v / (v + v₀))
Substituting the given values:
f = 1250 Hz
v = 343 m/s
v₀ = 6.50 m/s (since the boy is riding away from the car)
f' = 1250 * (343 / (343 + 6.50))
Calculating f':
f' = 1250 * (343 / 349.50) ≈ 1220.06 Hz
Now we have all the values to calculate vs:
vs = (f * v - f' * v) / f'
= (1250 * 343 - 1220.06 * 343) / 1220.06
≈ 86.69 m/s
Therefore, the frequency heard by the boy on the bicycle is approximately 1220.06 Hz.
To determine the frequency heard by the boy on the bicycle, we need to consider the Doppler effect. The Doppler effect is the change in frequency of a wave due to the relative motion between the source of the wave and the observer.
In this case, the car serves as the source of the sound wave, and the boy on the bicycle is the observer. The speed of sound is given as 343 m/s, the car's alarm frequency as 1250 Hz, and the boy's velocity as 6.50 m/s.
The general equation for the Doppler effect is:
f' = (v + vo) / (v + vs) * f
Where:
f' = observed frequency
v = speed of sound (343 m/s)
vo = velocity of the observer (boy on the bicycle) = 6.50 m/s
vs = velocity of the source (car) = 0 m/s (since the car is stationary)
Using this equation, we can calculate the frequency heard by the boy on the bicycle:
f' = (343 + 6.50) / (343 + 0) * 1250 Hz
f' = 349 * 1250 Hz
f' ≈ 436,250 Hz
Therefore, the frequency heard by the boy on the bicycle is approximately 436,250 Hz.