# How can I use the doppler effect equation?

Sep 8, 2015

It can be used for sound or light sources travelling relative to each other and resulting in the observer noting a different frequency to the one emitted by the source.
For source and observer moving towards each other, the observed frequency is higher than the emitted one, vice versa for the two moving away from each other.
I give 2 examples below.

#### Explanation:

Example 1:
Suppose that an ambulance is travelling at 30 m/s towards a stationary observer at an accident scene and emits a siren of sound wave frequency 400 Hz. Calculate the frequency that the observer hears. Take the speed of sound in air as 340 m/s.
Solution:
$f ' = f \left(\frac{v + {v}_{0}}{v - {v}_{s}}\right)$
$= 400 \left(\frac{340 + 0}{340 - 30}\right)$
$= 438 , 71 H z$

Example 2:
Suppose an observer in a spacecraft travels at a speed of 2x10^8 m/s towards a stationary red light emitting light of wavelength 660 nm. Calculate the frequency and colour of the light that the observer notices. Take the speed of light in air as 3x10^8 m/s.
Solution
$f ' = f \left(\frac{c + {v}_{0}}{c - {v}_{s}}\right)$
$= \frac{3 X {10}^{8}}{660 X {10}^{- 9}} \left(\frac{3 X {10}^{8} + 0}{3 X {10}^{8} - 2 X {10}^{8}}\right)$
$= 1 , 36 X {10}^{15} H z$
This corresponds to a wavelength of 220 nm which falls outside the visible spectrum of light and so the observer will see no colour at all.