# Doppler Shift Formula

## Doppler Shift

A Doppler shift is a phenomenon of a change in frequency based on the observer’s point of view. The most common analogy of this is standing on the side of the road and listen to a passing car. As the car approaches, there is a definitive sound. As the car passes, the sound changes to a lower frequency. This is called a Doppler Shift. There are two types of Doppler shifts:
• Red-Shift or a shift of frequency to a lower wavelength (away from the observer)
• Blue-Shift or a shift of frequency to a higher wavelength (toward the observer)

This is the equation for Doppler shift

$\frac{\Delta \lambda }{\lambda _{0}}=\frac{v}{c}$
$\Delta \lambda$Â = wavelength shift
$\lambda _{0}$Â = wavelength of the source not moving
v = velocity of the source
c = Speed of light
Apparent Frequency formula is given by
$f^{'}=\frac{(v+v_{0})}{(v-v_{s})}f$
f= actual frequency of the sound wave
f ‘ = observed frequency
v =speed of sound waves

$v_{0}$Â =velocity of observer

$v_{s}$Â = velocity of the source

### Solved Example

Question 1: A source and listener are moving towards each other with a speed of 54 km/hr. If the true frequency of sound emitted by the source is 500 Hz, calculate the observed frequency when both source and listener are moving towards each other.

Velocity of sound in air = 330 ms-1.

Solution:

Given: True frequency, f = 500 Hz,

Velocity of sound, vs = 54 km/hr = 54Ã—1000/3600Â  = 15 ms-1,

Velocity of listener,v0 = 15 ms-1

Source and observer moving towards each other

$f^{'}=\frac{(v+v_{0})}{(v-v_{s})}f$
$f^{'}=\frac{(330+15)}{(330-15)}500$

= [345/315]500

=1.095/500

f ‘=0.00219Hz

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