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:

Doppler shift formula

 = wavelength shift
 = wavelength of the source not moving
v = velocity of the source
c = Speed of light

Doppler Shift Formula of frequency change:

f' = \frac{V}{V - V_s}f

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.

f' = \frac{V}{V - V_s}f

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

Plugging the values in the equation,

f' = \frac{V}{V - V_s}f

⇒ f' = \frac{360}{360 - 3}440

⇒ f' = \frac{360}{357}440

⇒ f' = \frac{360}{357}440

⇒ f’ = 443 Hz .

Physics Related Formulas
Electric Field Formula Poynting Vector Formula
Gross Profit Formula Refraction Formula
Mass Formula Sound Intensity Formula
Capacitance Formula Uniform Circular Motion Formula
Centripetal Force Formula Thermal Expansion Formula
Distance Speed Time Formula Thermal Energy Formula
Ohms Law Formula Amperes Law Formula
Refractive Index Formula Horsepower Formula
Wavelength Formula Lattice Energy Formula
Stress Formula Length Contraction Formula

FAQs (Frequently Asked Questions)

1. State the cause of the doppler shift.

The Doppler effect is defined as the effect caused by a forth and of vibrations where there is a perceived higher change in speed for perceivers facing the source and an apparent downward change in frequency for perceivers facing away from the source.

2. State one significance of the Doppler Shift.

The Doppler effect for electrical signals of light leads either in crimson or colored shift in astronomy. The Doppler effect and radial velocity may be used to calculate the pace at which planets or galaxies are retreating or going to reach us.

3. How are sirens used in emergency vehicles as an application of the Doppler Shift?

The theory underlying the siren is that as it slides down from the spectator, it begins at a higher register than its static pitch, and when it retreats from the watcher, it begins at a lower frequency than its static pitch. It is commonly seen in emergency services.