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Non-Relativistic Doppler Effect – All You Need To Know

The concept around the Doppler effect is basically how much a wave stretches or bunches due to the speed it is travelling at.

The most common scenario you will experience the Doppler effect will be with an Ambulance. As you here the sirens approach you, the waves will have been ‘squished’ or compressed producing a higher pitch sound. As the ambulance moves past you, the waves are now stretched causing the pitch to decrease creating a high to low pitch. This is also the cases with F1 cars that move past at high velocities.

How the Doppler Effect Applies to Light

The information we already know:
• The original wavelength (λ) of the light approaching Earth from a distance sun. We know this because we can recreate the conditions of distance suns on Earth providing the wavelength of light the distance sun emits.
• Therefore, we know the λ which is the wavelength we receive on Earth – original wavelength.
From this, the proportion of the bunching can be equated to λ / λ.  This ultimately provides the equation:

λ / λ = v / c

Where v = velocity of the wavelength at which its moving and c being the speed of light which is 3×10^8 m/s. However, this equation only applies when v << c (when the velocity of the wavelength is much much smaller than the speed of light). As a general rule, the maximum velocity of the wavelength for the equation to work is 0.1c.

Detailed Explanation

Below is a picture of a stationary star emitting a wave or length λ:

If we know distance = speed x time and the time to emit one wave is △t, then λ = c△t.

The next diagram is of a moving star:

The wavelength λ is the same as the stationary star above. This time, the star is moving at a velocity of v. Therefore, λ  is the distance moved by the star. Therefore, using d = s x t, λ = vt. But, we know that t = λ / c from above. Therefore, λ = v x λ/c:

λ  / λ = v / c

Question: Why does this not take account of relativity?
Answer: Because t for a stationary star and t for a moving star were equated and they are not the same because t = γΤ.This is light clocks and time dilation which can be looked into more detail in an article on it in under Physics A2. The theory is that time is not a constant in our universe: instead, the speed of light is. Therefore, time slows down as you get closer to the speed of light. However, as the speed v is << (much much less than) c (speed of light), the value of γ will be extremely close to 1. Therefore, the formula is OK to use.

Summary

• The Doppler effect is when a wavelength is stretched or compressed due to the object of which is producing the wavelength is moving further away or closer to the observer.
• For speeds less than 0.1c, we can use the equation λ / λ = v / c to work out the proportion of bunching.

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