# Intuitively, what actually is the cause of resonance?

Please don't explain it mathematically. I have been searching for the reason for a long time.

I have watched Walter Lewin's video giving an example of resonance, but I didn't get the reason behind the intuition. I am confused if the reason exists.

• Related recent question Jan 28, 2021 at 15:15
• Have you ever pushed a friend or sibling or child on a swing? That's the intuition for resonance. You pushing on the swing is resonance. Have you ever tried to stop a swing? That's the opposite of resonance - that's noise cancellation Jan 28, 2021 at 20:05
• Nandani, it would help us if you gave us a bit more detail about the specific things you would like us to clarify - the answers are mostly explaining the notion of resonance itself, but maybe that's not what you're after? Lewin's demonstration is based around sound breaking a glass, so, maybe you're more interested in the specifics of that? E.g., would it help if the answers addressed how sound travels, and maybe what sound even is, how is it making the glass vibrate, etc? Jan 30, 2021 at 21:02
• Also, it would be helpful to us if you told us what's unclear about the answers posted - e.g. maybe it's not easy to see what's the connection with the swinging pendulum? Jan 30, 2021 at 21:02

For intuition I find it easier to start with a regular pendulum. Imagine a steel ball on a string hanging down. If you give it a push, it will start to swing back and forth.

Now if you, while the pendulum is swinging, give it another push in the same direction, it will matter where it is when you push it. If it is travelling in the opposite direction you are pushing it in (say, you push from left to right, then this would mean pushing when the pendulum is travelling right to left), you will slow the pendulum down. However, if you push it, when it is already travelling in that direction (so, push it from left to right when it is already travelling left to right), it will speed up.

Now say you push it periodically, that is, in regular time intervals. If you just choose a random interval to push the pendulum, you will sometimes push it to make it go faster, and sometimes to slow it down. Depending on the exact frequency you push it at, this will mostly cancel out.

If you, however, push it always when it is going left to right, it will speed up every single time you push it. But in order to push it at the same point in its period, the frequency you are pushing it in must match the frequency the pendulum is going in anyway. Conveniently, this frequency is independent of the amplitude (i.e. how high the pendulum is swinging) and only depends on properties of the system itself.1 This is called the natural frequency or resonant frequency of the system (there are nuances between these terms that don't matter in this context). So pushing at that frequency will lead to resonance and (without damping) the pendulum will swing higher and higher (its amplitude will become arbitrarily large).

The same is true for larger and more complicated systems, though they will ususally have multiple resonance frequencies.

1. This is strictly only true for harmonic oscillators, i.e. systems where the restoring force is proportional to the displacement; for a hanging pendulum this is only true for small angles, but for the sake of simplicity we'll ignore that in the context of this answer.

• I would add that this effect holds because the "natural frequency" is fixed, as it is given by material properties (given by the length of a pendulum or by the spring constant of a spring etc) so that your "pushing" does not change it and thus the effect is amplified every time. To maintain the oscillations at a fixed frequency even when you are pushing it it needs to swing at larger and larger amplitudes every time to compensate for the extra "energy" you gave it! Jan 27, 2021 at 23:10
• That's a good point that's strictly not even true for a hanging pendulum. But the answer was getting quite long so I figured I'd skip that part, since it was supposed to be about intuition and not exact solutions.
– noah
Jan 27, 2021 at 23:14
• There's more to it: if you push with the same frequency as the pendulum, but oppositely so it slows down, it will eventually stop and speed back up again but this time aligned to your pushes. So the system strengthens modes that have resonance, and eliminates modes that have anti-resonance. Jan 27, 2021 at 23:56
• Excellent example! @JalfredP You can assume that the natural frequency is fixed only for linear time-invariant systems. Behavior of nonlinear systems depends on the current state the system is in. Jan 28, 2021 at 7:19
• @causative “and eliminates modes that have anti-resonance” doesn't really make sense. Those are the exact same modes. It's just a matter of phase relation. If the system is undamped and (to good approximation) linear, then any input that doesn't exactly hit the resonance frequency will actually result in a beat: build up oscillation, then go out of phase and thus decrease again, stop and start from 0 once more... (There is also such a thing as “anti-resonance” in notch filters, but that's really just damped resonance that is mixed with the inverted signal.) Jan 28, 2021 at 15:25

If you have ever learned how to swing on a swing set then you have directly applied resonant forcing. By moving your body in the right way in time with the swinging motion, you can add more energy to your swing, thus going faster and higher. This is the basic idea of resonance, the word implies that something is "vibrating" at the same frequency as something else: in this case, the oscillating motion of the swing is resonating with the oscillating motion of your body.

If you push something when it is already going away from you, you cause it to go faster.

If you push something when it is coming toward you, you cause it to slow down.

Resonance is pushing something when it's going away from you, and pulling it when it comes toward you, over and over again, causing the energy of the push/pull to be transferred to the existing kinetic energy of motion instead of slowing down.

That is when the resonant frequency (time between forward and back motion) is in-phase with the push/pull. When it is out of phase with push/pull, one can do things like cancel sound (by exactly opposing the propagating sound wave, at the "resonant frequency," but out of phase).

• I like the simplicity of this answer, but I think not setting up the frame of reference a bit more could leave out folks who don't already have a mental picture of an oscillating or simple harmonic motion. Jan 28, 2021 at 20:16

Take a simple example of a musical cord, stretched between two pegs, at rest. If you pinch it a sound comes out, described by sinusoidal waves. This sound is characteristic of the length of the cord, and has a specific note dominant. When nobody touches it there is no sound.Then if an exactly the same cord is rung next to it, the quiet cord "resonates", the dominant sound coming out of it,though nobody touches it.

What is happening? Because sound is sinusoidal changes in air pressure traveling with the speed of sound in the air, the air pushes back and forth the cord and because it is the same length and type as the one playing, it starts vibrating in resonance, the energy coming from the incoming sound wave. A different length string plucked, will not raise the resonance of the one at rest ( in general, there could be harmonics). One needs the mathematics of sines and cosines to describe these waves .

The process is the same in all resonance effects. The objects to resonate need an incoming energy in phase ( in step) with the inherent frequency of the object that will resonate: the glass that breaks , or the step rhythm of soldiers that can break a bridge if in resonance with the structure.

• @DanielR.Collins yes, thank you. You see it is a greek word meaning cord(same root) in greek bu taken for music in english. Jan 28, 2021 at 5:27

Resonance can occur when objects have a 'restoring force'. Consider a spring for example. It has a resting state and if you perturb it by pulling on it tries to return to its resting state by creating a restoring force. It's common in nature that this restoring force gets bigger if you displace it more. So force $$\propto$$ displacement. If this proportionality happens then we have harmonic motion. If you give a harmonic system a kick it will oscillate with a particular frequency: it's natural frequency.

If you drive this system with a periodic force that doesn't match the natural frequency a sort of compromis happens. The system oscillates with the driving frequency but the oscillation either lags behinds or is ahead; It is out of phase with the driving frequency. Because it's out of phase the driver doesn't always put energy into the system. Sometimes the driving force is opposite to the velocity of the oscillator so this means energy will be drained out of the system. When the system has been driven for a while it has reached equilibrium. The energy put into the system by the driver matches the energy that is drained from the system either by being out of phase or by friction. At equilibrium the amplitude of the motion is constant.

When you drive at the natural frequency something interesting happens. The driving force is now always in phase with the oscillator. This means the driver always puts energy in the system and never drains it so the only way for energy to leave the system is by friction. The closer you are to resonance the higher the equilibrium amplitude. You can imagine that if you hit resonance in situations with little friction this can get out of hand quickly.

Many kinds of oscillators are governed by laws that mean that they oscillate with the same frequency (or nearly the same frequency) no matter what the amplitude of the oscillation is. If you raise a pendulum higher, it covers more distance with each swing, but it also moves faster at the bottom of the swing, so that the frequency stays the same (or at least close enough for practical purposes).

When you give something (oscillator or not) a push in the direction it's already going at that moment, it gains energy.

When something is oscillating, the only way to continually give it pushes in the same direction it's already going is for those pushes to share the same frequency (by reversing direction when the oscillator does, or by always pushing in the same direction but only doing it when the oscillator goes in the same direction).

A steady push in one direction will be going with the motion of the oscillator half the time, and against half the time, so it adds up to nothing.

A periodic push with a frequency that's different from the oscillator's frequency will spend part of its time "in phase" (pushing with the oscillator's motion) and part of its time "out of phase" (pushing against the oscillator's motion). Over a long enough period of time, these contributions add up to zero, and no net energy is added.

An ideal oscillator, driven at its natural frequency, would gain energy forever, and its amplitude would increase forever, but this isn't possible in the real world. Real oscillators all lose some amount of energy to the outside world with each cycle, the amount of energy lost increasing as the amplitude increases. A driven oscillator will reach a steady state when the rate of energy gain equals the rate of energy loss.

The simplest idea of resonance for me is that when you hit any object, be it a wooden table or a glass of beer, the transferred energy causes the object to vibrate at one point on its surface. This is called a natural frequency of the body.

If another object now produces a similar or the same periodic vibration (e.g. a guitar string, a loudspeaker membrane, etc.) with the same frequency, then a wave spreads out in the space around it, which in turn causes the other object to vibrate. This is called a resonating body and is the principle with which many musical instruments such as a guitar or a violin work.

In addition, in certain cases, a so-called resonance catastrophe can occur if the energy transferred to the body by the vibration is high enough to destroy the body. Also famous as when an opera singer manages to hold an accurate vibrato with such a tremendous volume (simply put the amplitude), that the wine glass will break in the end.

• This is a description, not an explanation, and not a good one. Vibration involves the whole object, not just a point. And there's nothing that makes sense as the antecedent of "This" in "This is called a natural frequency". Jan 29, 2021 at 1:10

This Action Lab video has an explanation of resonance that I found intuitive, but I can't say if it's correct.