# Doppler Shift Formula

## Doppler Shift Formula

The Doppler Shift, as applied to sound, is the change in frequency of a source as it travels. The frequency appears to grow as the source approaches the listener and decreases as the source moves away from them.

Doppler Shift is the phenomena in which the frequency of sound changes depending on the listener’s point of view. The Doppler Shift describes the degree of shift in the velocity of the source. We utilise the Doppler Shift formula to compute the velocity of stars. Let’s take a closer look at the Doppler shift formula.

### What is a Doppler Shift?

When it comes to sound, the Doppler shift refers to a source’s shift in frequency as a result of movement. When the source goes away from the listener, the frequency will appear to decrease, while it appears to increase when the source approaches the listener.

If the source is going in the direction of the listener, its velocity is positive; if it is moving in the other direction, it is negative. The listener’s velocity is positive when going in the direction of the source and negative when moving away from it. The frequency that the listener hears is higher than the frequency that the source is actually emitting.

There are two different forms of Doppler shift:

• Blue shift, which is a change in frequency to a higher wavelength that is directed toward the observer.
• Red shift, which is a change in frequency to a lower wavelength that is directed away from the observer.

### Doppler Shift Formula

When the source moves towards the listener, the wavelengths change to shorter ones. When the source moves away from the listener, the wavelengths change to longer ones. The Doppler shift formula for wavelength is:

$\frac{\Delta \lambda }{\lambda _{0}}=\frac{v}{c}$

$\Delta \lambda$ = wavelength shift
$\lambda _{0}$ = wavelength of the source not moving
v = velocity of the source
c = Speed of light

### Doppler Shift Formula of frequency change:

f frequency heard by the listener

fs frequency of the source

v velocity of sound

vs the velocity of the source

vL velocity of listener

The primary Doppler effect equation exists. But several circumstances can alter this equation. Depending on the observer’s or the sound source’s velocity, it is altered or adjusted. The various Doppler effect formulas will be shown in a number of circumstances or cases.

### Solved Examples for Doppler Shift Formula

Example 1: An ambulance approaches a person at a pace of 3 metres per second. Assume the ambulance siren’s frequency is 440Hz. Determine the frequency at which the observer hears the siren. (Sound velocity in air: 360 m/s).

Solution :

In this case, the source is moving towards the observer.

Given: f = 440Hz, V = 360 m/s and Vs = 3 m/s

Plugging the values in the equation,

⇒

⇒

⇒

⇒ f’ = 443 Hz .