Doppler effect - physics explained

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Can you guess what time it is? It is time for some science again and to be more precise, it's time for physics explained series. Today, I will write about an interesting little effect that happens with waves but before we start, here is the list of posts that I have already published in this series:

COLD BOILING WATER
HOW DO WE SEE COLORS
EVERYTHING IS MAGNETIC!
DIFFERENCE BETWEEN HEAT AND TEMPERATURE
CALCULATE THE SPEED OF LIGHT USING CHOCOLATE

This series is a lot of fun for me and I appreciate all your support. As I said, today I will talk about the Doppler effect. This phenomenon was first explained in 1842 by an Austrian physicist Christian Doppler after whom the effect got his name. The most common way we experience this effect in our daily lives is through sound waves so as most other people, I will explain it with sound too. Are you ready to have some fun with physics? Let's go!

Any Big Bang Theory fans out there? Remember this?

I love this show, it is one of my absolute favorites. In one of the episodes, the guys were invited to Penny's Haloween party and Sheldon was having troubles because no matter how hard he tried to hint it, people could not guess what he was dressed as. They kept calling him a zebra which was hilarious to me while the poor guy was expecting that everyone knows what Doppler effect is. Here is some help Shelly, I will try and explain it to them.

The Doppler effect is a change in the frequency. That change happens by virtue of relative motion between the source of the sound and the observer of that sound. You have heard this effect many times in your lives with ambulance vehicles, train whistles and any kind of sirens. When the sound source was approaching you, the pitch of it was much higher and when it was moving away from you, it was lower. This happens because the movement alters the wavelength which impacts the frequency.

Look at the gif image above. Wavelengths in front of the sound source are shorter so the wavefronts are much closer while the wavelengths behind it are bigger and the wavefronts are further apart. Do you see it?

The original frequency of the source does not change!

The police siren is producing the same sound waves all the time, you are hearing them with a higher or lower pitch because of distances changing.

There are 7 possible combinations here:

both source and the observer are stationary
observer is stationary, source is moving towards him
observer is stationary, source is moving away
source is stationary, observer is moving towards him
source is stationary, observer is moving away
source and the observer are moving towards each other
source and the observer are moving away from each other

The math is almost the same and if you understand how the wavelengths behave and what is their correlation to frequency, you will have no problems and be able to approach any situation so these seven combinations all roll into one where you just need to be a little more concentrated.

Stationary source and observer

When neither source or the observer are moving, there is no Doppler effect. The frequency that the source is producing is the same frequency the observer is hearing. It does not matter if the observer is in the front or in the back of the source.

There is a simple equation that connects frequency, velocity and wavelength. Frequency is the ratio of velocity and wavelength and in this case f(L) - frequency the listener hears and f(S) - frequency of the source are the same.

Moving source and/or observer

In the image above, the source is moving and we have two listeners, one in front and the other behind the source. Those two listeners will not hear the same pitch. The listener towards whom the source is moving will hear a higher pitch while the person behind will hear a lower pitch.

As I mentioned before, the listener could be moving too, what then? There is ONE FORMULA that fits all seven previously mentioned scenarios.

There are + and - signs in this formula one atop of the other. I have written them like this because velocities of source and observer can be either positive or negative. It is very important to assign the signs correctly. The first thing we have to remember is that the direction FROM SOURCE TO OBSERVER is always POSITIVE. We now only have to determine in which direction is what moving. As for the v=330 m/s, that is the speed of sound the source is producing in a vacuum. Since we do not live in a vacuum, there is a simple way for the sound speed to be approximated:

v = 330 m/s + 0.6 *T

T stands for temperature in degrees Celsius so for the 20 °C we would have the following:

v = 330 + (0,6*20) = 330 + 12 = 342 m/s

EXAMPLE 1. - moving away

Let's consider an example where the observer is left from the source and they are both moving. The observer is moving left and the source is moving right so they are actually moving away from each other. The direction from source to the observer is always positive and in this case that would be from right to left since the source is right from the observer.

observer's velocity is positive
source's velocity is negative

The reason that observer's velocity is positive is because he is moving from right to left going in the positive direction while the source is moving from left to right going in the negative direction so its velocity is negative.

EXAMPLE 2. - moving towards

Now let's see the opposite situation. The observer is again left from the source but now they are both moving towards each other. Since the direction from source to the observer is again from right to left, that is again our positive direction.

observer's velocity is negative
source's velocity is positive

Now the observer has negative velocity because he is moving from left to right which is the negative direction while the source has the positive velocity because it is going in the positive direction, from right to left.

Be honest, how many speeding tickets have you received so far? The reason why police knew you were going too fast is the Doppler effect. Police sends out radar waves and they are bounced off your car and reflected back to them. There is a computer built in the radar system that compares the outgoing frequency with the one that was reflected back and calculates the speed of your car. Do not hate the cops who gave you the ticket, do not even hate the Doppler effect and physics, just drive slower next time.

There are many applications of this effect, police measuring speed of the cars is only one of them. You can experience this effect whenever an ambulance vehicle is passing you by or you are visiting a train station. Whenever there is a sound source moving, there is a Doppler effect going on. Remeber:

When the observer and the sound source are moving away from each other, the pitch is lower
When the observer and the sound source are moving towards each other, the pitch is higher

What about Shelly?

The white spot on his chest represents the sound source and the white lines are wavefronts. Where the white lines are closer together, the black space between them is smaller. That spaces are wavelengths. Where the lines are further apart, there is larger space between them and the wavelengths are bigger. Wavelength and the frequency are inversely in proportion. The smaller the wavelength, the higher the frequency.

Want to learn more? Check out references:

Sound - ENCYCLOPEDIA BRITANNICA
The Doppler Effect - Physics Classroom
The Doppler effect by Matthew Schwartz
Does Motion Affect Sound? - Hearing Health

Until next time,
KEEP YOUR SMILE ON
and respect your inner genius!

If you are interested in something physics (or science in general) related, tell me and I would be happy to make a post about it and explained it. Promoting science and making it understandable gives me great joy, I would be happy to help you.