# How does resonance of waves work?

I finished reading my physics textbook chapters on waves and I think I understand how resonance works but I want to verify. PLEASE ;_______;

Simon Bridge
Homework Helper
The best way to gain understanding in this is to have a go explaining it to someone else - please tell us your understanding of how resonance works, then we can figure out how best to improve your understanding.

The best way to gain understanding in this is to have a go explaining it to someone else - please tell us your understanding of how resonance works, then we can figure out how best to improve your understanding.
from my understanding this is how I claim resonance works, please fix any errors
A source causes vibrations in the air which causes pressure changes and thus a wave, if that wave goes inside say a tube, some of the wave will get reflected by the surface walls of the tube, this reflected wave is inverted and if it is in phase with the source wave it produces a standing wave and thus resonance, because the standing wave is the sum of both the source wave and the reflected wave's amplitude in phase

Simon Bridge
Homework Helper
Close... the incomming wave is considered to be driving the system, which, in your example, is the tube.
The system prefers particular frequencies. You seem to have understood how that happens -the wave bounces back and forth variously reinforcing and cancelling, the overall effect depend on what the system is. There are lots of ways that the system ends up preferring particular frequencies. Think: pendulum.

If you imagine sending just a pulse at the tube, the pulse enters, travels the length of the tube, reflects, and comes back. When it reaches the open end again, part of the pulse reflects , repeating the cycle. Left at that, the reflected pulse gets smaller and smaller until its gone. But if you timed the next pulse so it enters the tube right when the first one was being reflected... and if you kept doing that...

As the driving frequency gets closer to a preferred frequency, the amplitude of the wave in the system gets bigger.
This phenomena is called resonance.

It happens anywhere you get an oscillator with an osscillating driving force... i.e. A mouse wants to get a heavy nut out of a deep bowl. It is not strong enough to lift it all the way, but can give it a shove so it rolls a bit up the sides. Can you see how the mouse needs to time the shoves to get the nut out?

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HiggsBoson1 and Jewish_Vulcan
Imagine the simplest case of resonance (IMO), a driven pendulum. If we first consider the pendulum, it will have it's preferred frequency, or natural frequency. What does this mean? This means that left swinging, it will have a time in it's motion when it reaches it's highest point, comes to a complete stop, and starts going the other way.

Now imagine that you want to drive this pendulum, that means you (or some machine) will apply a force to the pendulum, getting it to move in the direction you want. Let's assume you will apply some varying force force with a maximum magnitude which I will denote as F. Recall, that F = ma or m*dv/dt. This means that for your alloted force, and given mass you will be allowed to change its velocity by a given amount. The time at which you apply this maximum force is crucial, If you apply your maximum force in the -x direction when it is moving in the +x direction, then part of this force, or change in velocity (or change in momentum to be more precise), must be "wasted" in slowing down the pendulum before the remainder of it will be used to actually propel it in the direction you want it to go. If however you time it so that it will use its greatest force when the pendulum has already stopped then none of this maximum force will be "wasted" in stopping the pendulum, rather it will all go towards propelling it in the direction you want it to go. This is, to me, the best example of resonance. It shows up in many other places, but I think this model of thinking of it will get you a long way.

Lmk if I wasnt clear or if you have any other questions

Close... the incomming wave is considered to be driving the system, which, in your example, is the tube.
The system prefers particular frequencies. You seem to have understood how that happens -the wave bounces back and forth variously reinforcing and cancelling, the overall effect depend on what the system is. There are lots of ways that the system ends up preferring particular frequencies. Think: pendulum.

If you imagine sending just a pulse at the tube, the pulse enters, travels the length of the tube, reflects, and comes back. When it reaches the open end again, part of the pulse reflects , repeating the cycle. Left at that, the reflected pulse gets smaller and smaller until its gone. But if you timed the next pulse so it enters the tube right when the first one was being reflected... and if you kept doing that...

As the driving frequency gets closer to a preferred frequency, the amplitude of the wave in the system gets bigger.
This phenomena is called resonance.

It happens anywhere you get an oscillator with an osscillating driving force... i.e. A mouse wants to get a heavy nut out of a deep bowl. It is not strong enough to lift it all the way, but can give it a shove so it rolls a bit up the sides. Can you see how the mouse needs to time the shoves to get the nut out?
Good explaination, thank you for helping me understand the concept of resonance better.

Imagine the simplest case of resonance (IMO), a driven pendulum. If we first consider the pendulum, it will have it's preferred frequency, or natural frequency. What does this mean? This means that left swinging, it will have a time in it's motion when it reaches it's highest point, comes to a complete stop, and starts going the other way.

Now imagine that you want to drive this pendulum, that means you (or some machine) will apply a force to the pendulum, getting it to move in the direction you want. Let's assume you will apply some varying force force with a maximum magnitude which I will denote as F. Recall, that F = ma or m*dv/dt. This means that for your alloted force, and given mass you will be allowed to change its velocity by a given amount. The time at which you apply this maximum force is crucial, If you apply your maximum force in the -x direction when it is moving in the +x direction, then part of this force, or change in velocity (or change in momentum to be more precise), must be "wasted" in slowing down the pendulum before the remainder of it will be used to actually propel it in the direction you want it to go. If however you time it so that it will use its greatest force when the pendulum has already stopped then none of this maximum force will be "wasted" in stopping the pendulum, rather it will all go towards propelling it in the direction you want it to go. This is, to me, the best example of resonance. It shows up in many other places, but I think this model of thinking of it will get you a long way.

Lmk if I wasnt clear or if you have any other questions
Thank you for the helpful reply. you would get the highest amplitude when you push the swing while it is at the 0 potential energy position right?

Simon Bridge
Homework Helper
It does not matter for the question where you push the swing, so long as it is the same force and in the same direction. It's the timing that counts.
It's just easier to push the swing at one end of the cycle.

Thank you for the helpful reply. you would get the highest amplitude when you push the swing while it is at the 0 potential energy position right?

No, when the potential energy is at 0 then all of it's energy is in kinetic energy which means its moving as fast as it can and you dont want to do much then. You want to wait until all of its energy is in potential so it has as little kinetic energy as it can.

Edit: been meaning to say I love your username but what kind of name is Vulcan for a nice Jewish kid? ;-)

No, when the potential energy is at 0 then all of it's energy is in kinetic energy which means its moving as fast as it can and you dont want to do much then. You want to wait until all of its energy is in potential so it has as little kinetic energy as it can.

Edit: been meaning to say I love your username but what kind of name is Vulcan for a nice Jewish kid? ;-)
@Simon Bridge said that it does not matter where you push the swing as long as it is in the positive direction there will be resonance, you say that for max resonance you have to push the swing when the PE is max in the direction that it is in motion. One of you must be not completely correct but who is it? I chose my username for a few reasons, My friends used to call me spock and I like physics and star trek tos.

HiggsBoson1
@Simon Bridge said that it does not matter where you push the swing as long as it is in the positive direction there will be resonance, you say that for max resonance you have to push the swing when the PE is max in the direction that it is in motion. One of you must be not completely correct but who is it? I chose my username for a few reasons, My friends used to call me spock and I like physics and star trek tos.

I think you are confusing when and where. As he says "its the timing that counts"

Simon Bridge