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How can I use the doppler effect equation?

Answer 1

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.

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((v+v_0)/(v-v_s))# #=400((340+0)/(340-30))# #=438,71 Hz#

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((c+v_0)/(c-v_s))# #=(3X10^8)/(660X10^(-9))((3X10^8+0)/(3X10^8-2X10^8))# #=1,36X10^(15) Hz# 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.

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Answer 2

Layla Ahmed

You can use the Doppler effect equation to calculate the observed frequency of a wave when the source or the observer is in motion relative to each other. The equation is given by:

f' = f * (v ± vo) / (v ± vs)

Where:

f' is the observed frequency
f is the frequency of the source
v is the speed of sound in the medium
vo is the velocity of the observer relative to the medium (positive if moving towards the source, negative if moving away)
vs is the velocity of the source relative to the medium (positive if moving away from the observer, negative if moving towards)

You plug in the known values and solve for the observed frequency.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.