# Tag Info

### Intuitively, what actually is the cause of resonance?

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 ...
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### Why is Microwaved mac & cheese burnt where they touch?

I get the same thing reheating some discs of glazed carrots. And there are several videos of folks doing this intentionally with grapes. An article published last year in PNAS says this will happen ...

### What is a linear system?

A linear system is a physical system responding to an external stimulation in a manner which is proportional to the amplitude of said stimulation. Stated otherwise, it is the study of a class of ...
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### What is the essential difference between a resonance and a particle?

A resonance (in the particle physics or related physics sense) and an unstable particle is exactly the same thing. The object has some complex mass and the imaginary part determines the decay width (...
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### How does a guitar work?

The string oscillations are mainly transverse (a standing wave). The string motion causes the tension to oscillate thus applying a varying force on the guitar top through the bridge and saddle. The ...

### Why do string instruments need hollow bodies?

The soundboard is the crucial component in acoustical amplification of string vibrations. The strings pass over the bridge, which is solidly attached to some part of the soundboard. A vibration at the ...

### Is resonance a general property of second-order differential equations?

Consider the second order differential equation \begin{align} f'' - \alpha^2 f = C \cos(\omega t) \end{align} with $\alpha$ a real constant. (Note the sign of the second term, which makes this ...
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### Why does resonance occur at only standing wave frequencies in a fixed string?

One way to explain it is to look at the string as a waveguide. You can send wave packets over the string, and they're reflected at the ends: Now, you can send in wave packets repeatedly rather than ...
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### Why does plucking a string produce harmonics instead of a pulse?

It does produce a pulse. However, the speed of sound in a string is very large so the pulse reaches the ends of the string very quickly. This means that in a second many reflections occur and you only ...

### ODE solutions for a driven oscillator in higher resonance modes

An oscillating system may have numerous resonances, but not that system! That ODE represents a driven harmonic oscillator with exactly one resonant frequency and, indeed, if you apply an out-of-...
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### Why are the closed and open ends of an organ pipe nodes and anti-nodes?

There are two ways to describe a sound wave. One is in terms of displacement of the medium and the other is in terms of pressure. This simple diagram shows that tthe two descriptions are $90^\circ$ ...

### Non-resonant but efficient frequencies

First I'll try to explain why the amplitude vs frequency diagram only has one maximum, then I'll go back to why this seems to contradict your intuition. Let's take the simplest forced oscillator ...

### Why is Microwaved mac & cheese burnt where they touch?

@BowlOfRed hit on it solidly. The noodles are acting as waveguides, because of their size and shape. Where they meet, a contiguous surface is created, but with a much higher resistivity, as it's a ...
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### Forced Oscillation Explained with Violin String

In musical instruments, none of the excitations, whether by bowing, plucking, reed vibration, lip vibration, striking, etc, are sinusoidal methods. Therefore, they all, by Fourier's theorem are ...
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### Can't understand Resonance in an Air Column

An air column of given length has many resonant frequencies. These are called the fundamental and the harmonics. The fundamental has the longest wavelength that can fit in the column and satisfy the ...
We can model a short building as a uniform cuboid of density $\rho$ occupying the region $$0 \le x \le L_x$$ $$0 \le y \le L_y$$ $$0 \le z \le L_z$$ with its mass given by M = \rho V = \rho A L_z = ...