A factory siren emits a sound at 900hz.what frequency will be heard by the driver of a car traveling at 100km.h away from the factory?
Help me please!
Vd=100,000m/1h * 100000m/3600s=27.8 m/s
= Velocity of driver.
Fd = ((Vs-Vd)/(Vs+Ve))*Fe
Fd = ((343-27.8)/(343+0))*900Hz
Fd = (315.2/343) * 900 = 827 Hz = Freq.
heard by driver.
Vs = Velocity of sound in air.
Ve = Velocity of the sound emitter
(siren).
Fe = Freq. emitted.
To determine the frequency heard by the driver of a car, we need to take into account the Doppler effect. The Doppler effect describes the change in frequency of a wave when there is relative motion between the source of the wave and the observer.
The formula to calculate the observed frequency (f') due to the Doppler effect is:
f' = f * ((v + vā) / (v + vs))
Where:
- f is the frequency emitted by the source (900 Hz in this case).
- v is the speed of sound in air (approximately 343 m/s).
- vā is the speed of the observer (car) in meters per second.
- vs is the speed of the source (factory siren) in meters per second.
Here, we are given the speed of the car, which is 100 km/h. To convert this to meters per second, we need to divide by 3.6:
vā = (100 km/h) / 3.6 ā 27.78 m/s
Since the factory siren is stationary, the speed of the source (vs) is considered to be zero.
Now we can substitute the known values into the formula:
f' = 900 Hz * ((343 m/s + 27.78 m/s) / (343 m/s + 0 m/s))
After calculating this, we find that the observed frequency (f') heard by the driver of the car is approximately 869 Hz.
Therefore, the frequency heard by the driver of the car traveling 100 km/h away from the factory would be around 869 Hz.