# Doppler Effect Question regarding wavelength changing

In summary, the listener is hearing a frequency of 779 Hz and the wavelength of the sound wave is equal to the speed of sound plus the speed of the wind plus the speed of the source, divided by the new frequency.

## Homework Statement

A listener L hears the siren from a moving police car ,S, which is moving away from the listener with a speed of v = 20.0 m/s. The listener is moving at 10.0 m/s towards the car. There is a wind blowing with a speed of v(wind)= 10.0 m/s from S to L. The siren is emitting sound at a frequency (f) of 800 Hz. The velocity of sound in air is 343 m/s. Calculate the frequency (f') heard by the listener and the wavelength (λ) of that wave.

## Homework Equations

f' = f(v +/- vD) / (v -/+ vS)
v = fλ

## The Attempt at a Solution

Finding the new frequency is easy:

f' = (800hz)(343+10+ 10)/(343+10+20)
f' = 779 Hz. But now for finding the wavelength I'm confused.
I know it's λ = v/f'

but is it:
v = 343m/s (the speed of sound in still air)
v= 343+10 m/s (the speed of sound + the speed of the wind)
v= 343+10+20 m/s (the speed of sound + the speed of the wind + the speed of the source)
or something else?

Any help would be much appreciated.

Last edited:
The wavelength heard by the listener is the frequency of the sound divided by the speed the wave is passing the listener.

Simon Bridge said:
The wavelength heard by the listener is the frequency of the sound divided by the speed the wave is passing the listener.

My apologies, I put the wrong question (I had v = f/λ when it should be v= fλ); I fixed this up now.

But by your statement would be the last option I suggested? λ = (speed of sound + speed of wind + speed of source)/(new frequency)?

## 1. How does the Doppler Effect affect the wavelength of sound?

The Doppler Effect is the change in frequency and wavelength of a wave as the source or observer moves. This means that as a sound source moves towards an observer, the wavelength of the sound waves becomes shorter, resulting in a higher pitch. Conversely, as the source moves away from the observer, the wavelength becomes longer and the pitch becomes lower.

## 2. What is the formula for calculating the change in wavelength due to the Doppler Effect?

The formula for calculating the change in wavelength is given by λ' = λ(v ± vr)/(v ± vs), where λ is the original wavelength, v is the speed of sound, vr is the velocity of the receiver, and vs is the velocity of the source.

## 3. How does the Doppler Effect apply to light waves?

The Doppler Effect also applies to light waves, but instead of affecting the wavelength, it affects the frequency. As a light source moves towards an observer, the frequency of the light waves increases, resulting in a blue shift. On the other hand, as the source moves away, the frequency decreases and a red shift occurs.

## 4. What factors can influence the perceived change in wavelength due to the Doppler Effect?

The perceived change in wavelength due to the Doppler Effect is influenced by the relative velocities of the source and observer, as well as the speed of the wave. Additionally, the direction of the source's movement in relation to the observer also plays a role.

## 5. How is the Doppler Effect used in real-life applications?

The Doppler Effect has various real-life applications, including in medical ultrasound imaging to measure blood flow, in weather radar to detect the movement of storms, and in astronomy to determine the speed and distance of stars and galaxies. It is also used in police speed guns and in navigational systems for ships and aircraft.

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