Two cars have identical horns, each emitting a frequency of f= 395 hz. One of the cars is moving with a speed of 12 m/s toward a bystander waiting at a corner, and the other car is parked. The speed of sound is 343 m/s. what is the beat frequency heard by the bystander?
Doppler-effect.
At source approaching
f(observed) = [v/(v-u)] •f(source),
f(observed) =
= [343/(343-12)] •395=409.3 Hz
f(beat)= f(observed)=f(source)=
=409.3-395=14.3 Hz
Well, it seems like this bystander is in for a musical treat! Let's get down to business and calculate the beat frequency.
The formula for calculating the beat frequency is:
beat frequency = |f1 - f2|
We're given that both cars have identical horns, emitting a frequency (f) of 395 Hz. However, one car is moving towards the bystander with a speed (v) of 12 m/s, while the other is parked.
Now, thanks to the Doppler effect, the frequency heard by the bystander will differ due to the motion of the car. The Doppler effect formula for a moving source towards an observer is:
f' = (v + vo) / (v +vs) * f
Where:
f' = frequency observed by the bystander
v = speed of sound (343 m/s)
vo = velocity of the observer (0 m/s, since the bystander is stationary)
vs = velocity of the source (12 m/s, since the car is moving towards the bystander)
Plugging in the numbers:
f' = (343 + 0) / (343 + 12) * 395 Hz
f' = 343 / 355 * 395 Hz
f' ≈ 380.7 Hz
So, the frequency heard by the bystander from the car in motion is approximately 380.7 Hz.
Since the beat frequency is the absolute difference between the two frequencies, we have:
beat frequency = |395 Hz - 380.7 Hz|
beat frequency ≈ 14.3 Hz
So, the clown car's horn will be producing a beat frequency of approximately 14.3 Hz for the bystander to enjoy!
To find the beat frequency heard by the bystander, we need to consider the Doppler effect. The Doppler effect relates the observed frequency of a sound wave to the frequency emitted by the source and the relative motion between the source and the observer.
In this case, one car is parked, so its frequency remains at 395 Hz. The other car is moving toward the bystander, causing a change in frequency due to the Doppler effect. Let's calculate this change in frequency step by step:
1. Find the frequency detected by the stationary car (the bystander):
The frequency detected by the stationary car can be calculated using the formula for the Doppler effect:
f' = (v + vs) / (v + vr) * f,
where f' is the detected frequency, f is the emitted frequency, v is the speed of sound, vs is the speed of the stationary car (0 m/s), and vr is the speed of the moving car (-12 m/s).
Substituting the values:
f' = (343 + 0) / (343 - 12) * 395 = 417.78 Hz.
Therefore, the frequency detected by the stationary car (the bystander) is 417.78 Hz.
2. Calculate the beat frequency:
The beat frequency is the difference between the frequencies of the two sound sources. In this case, it is the absolute difference between the frequency emitted by the parked car (395 Hz) and the frequency detected by the stationary car (417.78 Hz):
Beat frequency = |417.78 Hz - 395 Hz| = 22.78 Hz.
Therefore, the beat frequency heard by the bystander is approximately 22.78 Hz.
The given are (a) the speed of sound, which is 395 m/s, (b) the velocity of the moving source, which is 12 m/s, and (c) the frequency of the sound both cars are emitting, which is 395 Hz.
Let's assume that f{o} is the frequency the observer can hear and f{s} is the frequency the source emits, Vs is the velocity of the moving source, and v is the speed of sound.
The equation for a source moving towards an observer is f{o} = f{s} x (1- (Vs÷v))
f{o} = 395 Hz x (1 - (12 m/s ÷ 343 m/s))
f{o} = 381.180758 Hz
To compute for the beat frequency, let's assume that f{beat} is the beat frequency:
f{beat} = f{a} - f{b}; where f{a} is the larger of the two.
f{beat} = f{a} - f{b}
f{beat} = 395 Hz - 381.180758 Hz