At the Indianapolis 500, you can measure the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a factor of 2.40 as it goes by on the straightaway. How fast is it going? (assume speed of sound is 343 m/s).
I don't know where to start. I tried setting frequency2 = x(frequency1), where x=-2.4, but I don't know. Does anyone have suggestions? Thanks
I think I would use the doppler formula.
Yes, you are on the right track! To solve this problem, you can indeed use the Doppler formula to relate the change in frequency to the relative velocity between the source of the sound (car) and the observer (you).
The Doppler formula for sound moving in a medium is given by:
f2 = (v + vr) / (v + vs) * f1
Where:
f1 is the original frequency of the sound in Hz
f2 is the observed frequency of the sound in Hz
v is the speed of sound in the medium (343 m/s for air)
vr is the velocity of the receiver (you) relative to the medium (positive if moving towards the source, negative if moving away)
vs is the velocity of the source (car) relative to the medium (positive if moving towards you, negative if moving away)
In this case, since the sound drops in frequency as the car goes by, you can assume that the car is moving away from you. Therefore, vs (the velocity of the source) would be negative.
Now, you can substitute the given values into the formula and solve for the velocity of the car. Let's assume the original frequency f1 is known.
f2 = 1/2.40 * f1
Now, given the values of vs = -x and v = 343 m/s, we can rearrange the formula to solve for x:
1/2.40 = (343 + x) / (343 - x)
Solving for x using this equation will give you the relative velocity of the car.