Man stands out on the street with a frequency meter. A police car drives by with the sirens on and the frequency of the sounds measures 800 Hz when it get close but 600 Hz when the car goes away.
a) What is the speed of the police car?
b) What is the actual frequency of the sirens ?
To determine the answers to the given questions, we can use the Doppler effect equation. The Doppler effect describes the change in frequency of a wave (in this case, sound) as the source of the wave (the police car) moves relative to the observer (the person with the frequency meter).
The equation for the Doppler effect is as follows:
f' = [(v + v₀) / (v - vₛ)] * f
Where:
f' is the observed frequency
f is the actual frequency of the source
v is the speed of sound
v₀ is the speed of the observer (in this case, the person with the frequency meter)
vₛ is the speed of the source (in this case, the police car)
Now let's solve the questions:
a) What is the speed of the police car?
To find the speed of the police car, we can use the information that the frequency measured when the car approached was 800 Hz and the frequency measured when it moved away was 600 Hz.
We know that the observed frequency when the car approached is given by:
800 Hz = [(v + v₀) / (v - vₛ)] * f
And the observed frequency when the car moved away is given by:
600 Hz = [(v + v₀) / (v - vₛ)] * f
By dividing these two equations, we can eliminate the variables v and f:
(800 Hz / 600 Hz) = [(v + v₀) / (v - vₛ)] / [(v + v₀) / (v - vₛ)]
Simplifying this equation gives:
4/3 = 1
This equation does not hold, which means there is an error in the calculations or the given data. Please double-check the values provided for the observed frequencies.
b) What is the actual frequency of the sirens?
The actual frequency of the sirens can be found by using the observed frequencies when the car approached and moved away, along with the speed of sound and the formula for the Doppler effect.
However, since the value of the actual frequency (f) is not given in the question, we cannot determine it without additional information.
Please provide the value of the actual frequency (f) of the sirens to calculate the answer.