# Doppler Effect Relative Motion

• anhhuyalex
In summary, the formula for calculating the detected frequency from the source frequency takes into consideration the velocities of the source and detector relative to the medium. This is because the medium provides an absolute reference point and the speed of the wave is constant relative to the medium. In cases where the speed of the source is faster than the speed of the wave in the medium, a sonic boom or shock wave is generated and the Doppler formula does not apply.
anhhuyalex
To calculate the detected frequency from the source frequency, we use this formula:

${ f }_{ D }=\frac { v\pm { v }_{ D } }{ v\pm { v }_{ s } } { f }_{ s }$

where ${v}_{s}, {v}_{D}$ are velocities of the source and the detector respectively with reference to the medium. My question is why do we consider motion relative to the medium? Wouldn't a detector moving at 3 m/s receiving sound from a source moving at 8 m/s in the same direction detect the same frequency as a stationary detector receiving sound from a source moving at 5 m/s? However, from the above equation, that is not true. Thanks for taking your time to answer.

The reason is that the waves appear to be hitting you at with a speed v + vD + vs when in fact relative to a stationary observer with no velocity the waves are only traveling with a speed v.

Suppose you were measuring the intervals of water waves coming at you on a lake. You are in one boat and your friend is in another boat a distance away. The lake is still and there are no waves on it except for the ones that your friend can create by hitting his oar paddle on the water.

You agree that if your friend moved toward you with a speed vs (say he had a small motor that generated negligible waves compared to the oar paddle ones) that the frequency of the paddle oar waves hitting you would increase as his speed increases, right? You would bob up and down even more.

Now if you in turn started your small motor and moved towards your friend with a speed vD then the waves would seem to be coming in even faster. I'm sure you have experienced this if you have ever been on a speed boat before.

This is the equivalent of an increased frequency caused by a Doppler shift. You actually can't tell how fast the waves are moving (v) unless you also know your friend's and your own speeds. This is because the apparent speed would be v + vs + vD = λ*fD where λ would be the measured length of the wave.

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The formula is correct. The speeds are measure relative to the medium because the medium iks carrying the waves. The wave speed is constant relative to the medium. Your intuition is based on the relativity of motion which doesn't apply here since there is a medium

Why doesn't it apply just because of a medium? Since all motion are relative anyway, why is it that we need to consider the velocities from the reference of the medium instead of considering the velocities from the reference of the source or the detector?

You understand that the speed of a wave v is constant in the medium? If you accept that premise then the only thing that could possibly change the frequencies is the relative speeds between the source and detector.

What would happen if the speed of the wave is less than the speed of the source when the source is moving towards the detector? That would make a negative value for the denominator, wouldn't it, while the numerator is positive? Then, the frequency is going to be negative. Is that possible?

If something moves with a speed (vS) that is faster than the speed a wave propagates in a medium (v) then the object has broken the sound barrier and generates a shock wave with a speed =vS.

The Doppler shift equation does not apply in this case. My guess is that you would first feel the sonic boom then hear the unshifted regular sound waves moving at speed v with a frequency fS.

1 person
anhhuyalex said:
Why doesn't it apply just because of a medium? Since all motion are relative anyway, why is it that we need to consider the velocities from the reference of the medium instead of considering the velocities from the reference of the source or the detector?

It doesn't apply because the medium provides an absolute referential. Relativity of motion requires all the relevant elements of a problem to change their speed by the same amount. If you are in a moving car with closed windows it feels like you're sitting still. Everything is moving along at the same speed, including the air. Than relativity of motion applies. But if open the window than you can tell the difference between a moving car and a stopped car (Just feel the wind). In order for the relativity of motion to apply in the Doppler effect example you must carry the air along with you. But that's not the situation described by the formula.

anhhuyalex said:
What would happen if the speed of the wave is less than the speed of the source when the source is moving towards the detector? That would make a negative value for the denominator, wouldn't it, while the numerator is positive? Then, the frequency is going to be negative. Is that possible?

In that case you get a sonic boom AKA shock wave AKA bow wave like the one you see at the wake of a boat. The Doppler formula doesn't apply. There is no wave between you and the source if the source is moving faster than the wave.

## What is the Doppler Effect?

The Doppler Effect is a phenomenon that occurs when there is a change in frequency or wavelength of a wave as an observer moves relative to the source of the wave. This can be observed in various forms of waves, such as sound and light.

## How does relative motion affect the Doppler Effect?

Relative motion between the source of the wave and the observer can cause a shift in the frequency or wavelength of the wave. If the source and observer are moving towards each other, the frequency and wavelength will appear to be higher. If they are moving away from each other, the frequency and wavelength will appear to be lower.

## What are some real-world examples of the Doppler Effect?

One common example of the Doppler Effect is the change in pitch of a siren as an ambulance or police car passes by. Another example is the redshift observed in light from distant galaxies due to the expansion of the universe.

## How is the Doppler Effect used in science and technology?

The Doppler Effect is used in various fields, such as astronomy, meteorology, and medical imaging. It is also used in technologies such as Doppler radar, which can detect the speed and direction of moving objects through the analysis of frequency shifts in reflected waves.

## What is the difference between the Doppler Effect and the Doppler Shift?

The terms "Doppler Effect" and "Doppler Shift" are often used interchangeably, but there is a slight difference. The Doppler Effect refers to the change in frequency or wavelength of a wave due to relative motion, while the Doppler Shift specifically refers to the change in frequency of electromagnetic waves, such as light.

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