Open In App

Doppler Shift Formula

Improve
Improve
Like Article
Like
Save
Share
Report

When it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when it is traveling away from the listener, its velocity is negative. If the listener is traveling toward the source, its velocity is positive; if the listener is going away from the source, its velocity is negative. The frequency perceived by the ear is greater than the frequency emitted by the source.

 

There are two forms of Doppler shift: redshift, which is a change in frequency to a lower wavelength that implies away from the observer, and blue shift, which is a change in the frequency to longer wavelengths that indicates towards the observer.

Doppler Shift Formula

f = f_s\left(\dfrac{v + v_l}{v - v_s}\right)

where,

  • fs denotes the frequency of the source of the sound
  • v denotes the velocity of sound
  • vs denotes the velocity of the source
  • vL denotes the velocity of listener

Sample Problems

Problem 1: An object at 70 m/s is producing frequency at 100 Hz. Find the frequency of the sound heard by a person in front of the object.

Solution:

Given that,

v = 343 m/s

vs = 70 m/s

fs = 100 Hz

vL = 0 m/s

Therefore, by the formula of Doppler shift: 

\begin{aligned}f &= f_s\left(\dfrac{v + v_l}{v - v_s}\right)\\&=100\times \frac{343 + 0}{343 - 70}\\&= 125.64 \text{ Hz}\end{aligned}

Problem 2: An object at 90 m/s is producing frequency at 120 Hz. Find the frequency of the sound heard by a person in front of the object.

Solution:

Given that, 

v = 343 m/s

vs = 90 m/s

fs = 120 Hz

vL = 0 m/s

Therefore, by the formula of Doppler shift: 

t\begin{aligned}f &= f_s\left(\dfrac{v + v_l}{v - v_s}\right)\\&=120\times \dfrac{343 + 0}{343 - 90}\\&= 135.57 \text{ Hz}\end{aligned}

Problem 3: State the cause of the doppler shift.

Solution:

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.

Problem 4: State one significance of the Doppler Shift.

Solution:

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.

Problem 5: How are sirens used in emergency vehicles as an application of the Doppler Shift?

Solution:

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.


Last Updated : 04 Feb, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads