Question about doppler effect:

How do you solve when it gives you percentage value? (Q 1) How do you calculate for doppler effect when the listener is moving instead of the source of sound? (Q 2)

Questions
1. As a racing car zooms by you, its pitch decreases by 20%. If the speed of sound is 345 m/s, how fast is the car travelling?

2. Find the apparent frequency of a person moving at 30 m/s hears if she is moving a) toward a stationary siren with frequency 1800 Hz. b) away from a stationary siren with a frequency 1800Hz

To solve these questions that involve the Doppler effect with percentage values, you can follow the steps below:

For Question 1:
1. Identify the given information: In this case, the information given is that the pitch (frequency) decreases by 20%, and the speed of sound is 345 m/s.
2. Start by defining the initial frequency of the sound wave emitted by the car. Let's call it f0.
3. Since the pitch (frequency) decreases by 20%, you can calculate the final frequency, which we'll call f, using the formula:
f = f0 - 0.20 * f0
This formula represents a decrease of 20% in frequency.
4. Now, you need to relate the change in frequency to the motion of the car. The Doppler effect formula for this case is:
f/f0 = (v + v0) / (v + vs)
where:
f is the final frequency of the sound wave heard by the observer (f in step 3).
f0 is the initial frequency of the sound wave emitted by the car (frequency before any changes).
v is the speed of sound (given as 345 m/s).
v0 is the speed of the observer (car) with respect to the medium (unknown).
vs is the speed of the source (car) with respect to the medium (unknown).
5. Rearrange the formula from step 4 to solve for v0 (speed of the car):
v0 = ((f/f0) - 1) * v - vs
6. Plug in the values you know into the formula from step 5 and solve for v0.

For Question 2:
The calculation is similar to Question 1, but with a slight difference in the Doppler effect formula. The formula is as follows:
f/f0 = (v + v0) / (v - vs)
The only difference is that the sign before vs is negative because the listener is moving instead of the source.

Here's how you would solve the two parts of Question 2:

a) When the listener is moving toward the stationary siren:
1. Identify the given information: The listener's velocity is 30 m/s, and the siren's frequency is 1800 Hz.
2. Use the above Doppler effect formula, with the given values, to find the apparent frequency (f):
f/f0 = (v + v0) / (v - vs)
3. Rearrange the formula from step 2 to solve for f:
f = ((v + v0) / (v - vs)) * f0
4. Plug in the values you know into the formula from step 3 and solve for f.

b) When the listener is moving away from the stationary siren:
1. Follow a similar process to step a, but with the Doppler effect formula adjusted for the listener moving away from the source.

Remember to always check the units and signs of your calculations to ensure accuracy.