The siren on an ambulance is emitting a sound whose frequency is 2421 Hz. The speed of sound is 343 m/s. (a) If the ambulance is stationary and you (the "observer") are sitting in a parked car, what are the wavelength and the frequency of the sound you hear? (b) Suppose that the ambulance is moving toward you at a speed of 28.5 m/s. Determine the wavelength and the frequency of the sound you hear. (c) If the ambulance is moving toward you at a speed of 28.5 m/s and you are moving toward it at a speed of 12.6 m/s, find the wavelength and frequency of the sound you hear.

A. wavelength= 343/ frequency of siren

frequency= 343/ wavelength

B. Frequency= 343* frequency of siren/ (343-velocity of ambulance)

wavelength= 343/ frequency you found above

C. Frequency= (343+velocity of your car)*frequency of siren / (343- velocity of ambulance)

wavelength= 343/ frequency you found above

The formula you will need to answer all of these problems can be found at

http://en.wikipedia.org/wiki/Doppler_effect

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To solve this problem, we can use the formula for the Doppler effect, which relates the observed frequency of a sound source to the actual frequency and the relative motion between the source and observer.

The Doppler effect formula for the observed frequency when the source is moving towards the observer is:

f' = (v + vo) / (v + vs) * f

where f' is the observed frequency, f is the actual frequency, v is the speed of sound, vo is the velocity of the observer, and vs is the velocity of the source.

Now let's go through each part of the problem:

(a) If the ambulance is stationary and you (the "observer") are sitting in a parked car, the wavelength and frequency of the sound you hear are the same as the actual frequency of the ambulance siren, since there is no relative motion between the source and the observer.

So, the wavelength is the speed of sound divided by the frequency:

wavelength = v / f
wavelength = 343 m/s / 2421 Hz = 0.142 meters

(b) If the ambulance is moving towards you at a speed of 28.5 m/s, we can use the Doppler effect formula to find the observed frequency and wavelength.

The observed frequency can be calculated as:

f' = (v + vo) / (v + vs) * f
f' = (343 m/s + 0 m/s) / (343 m/s + (-28.5 m/s)) * 2421 Hz
f' = 343 / 314.5 * 2421 Hz
f' ≈ 2649.52 Hz

To find the observed wavelength, we can use the formula:

wavelength' = v / f'
wavelength' = 343 m/s / 2649.52 Hz ≈ 0.1293 meters

(c) If both the ambulance and the observer are moving towards each other, we need to consider both their velocities in the Doppler effect formula.

Using the same formula as before, the observed frequency can be calculated as:

f' = (v + vo) / (v + vs) * f
f' = (343 m/s + 12.6 m/s) / (343 m/s + (-28.5 m/s)) * 2421 Hz
f' = 355.6 / 314.5 * 2421 Hz
f' ≈ 2729.51 Hz

To find the observed wavelength, we can use the formula:

wavelength' = v / f'
wavelength' = 343 m/s / 2729.51 Hz ≈ 0.1259 meters

In summary:
(a) When the ambulance is stationary, the wavelength and frequency you hear are the same as the actual frequency.
Wavelength = 0.142 meters, Frequency = 2421 Hz

(b) When the ambulance is moving towards you at a speed of 28.5 m/s.
Wavelength = 0.1293 meters, Frequency ≈ 2649.52 Hz

(c) When both the ambulance and the observer are moving towards each other.
Wavelength = 0.1259 meters, Frequency ≈ 2729.51 Hz