93
votes
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 ...
- 10.1k
59
votes
Accepted
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 ...
- 37.1k
55
votes
Does amplitude really go to infinity in resonance?
$x(t)$ does not instantaneously go to infinity; the case $\omega=\omega_0$ needs special care. I think an answer directly from the math will help. The driven SHM equation of motion is
$$\tag{1}
x''+\...
- 921
50
votes
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Why do string instruments need hollow bodies?
Yes, the room has a lot of air, but most of it isn't in direct contact with the vibrating string. In order for the string to make much sound, it needs to transfer some of its energy to the surrounding ...
- 10.6k
38
votes
Why does blowing a whistle in someone's ear damage it more than blowing directly in their ear? Won't the whistle reduce overall energy?
The eardrum is damaged if it is stretched too far. The stretching is caused by an imbalance of pressure on either side of the eardrum. Blowing into the ear creates a stream of air that tries to enter ...
- 23.5k
30
votes
Intuitively, what actually is the cause of resonance?
If you have ever learned how to swing on a swing set then you have directly applied resonant forcing. By moving your body in the right way in time with the swinging motion, you can add more energy to ...
- 3,560
29
votes
Accepted
Why does pitch increase when you blow harder into a whistle?
I don't believe the other answers are correct. FGSUZ describes pushing air out of a tube, which sort of plays a little part, but not the whole story.
The way woodwind instruments produce sound, is ...
- 450
26
votes
How does the string of an acoustic guitar transfer energy to the guitar's body?
If the impedance of the string were truly matched to that of the soundboard, then a string vibration would be completely absorbed into the soundboard with no reflection and the string would almost ...
- 83.7k
24
votes
Does amplitude really go to infinity in resonance?
Your solution
$$x(t)=\frac{F_0}{m(\omega_0^2-\omega^2)}\cos(\omega t) \tag{1}$$
was derived from the differential equation
$$m(\ddot{x}+\omega_0^2x)=F_0\cos(\omega t) \tag{2}$$
So the forced ...
- 32.4k
23
votes
Why does pitch increase when you blow harder into a whistle?
This is a very interesting phenomenon.
Roughly speaking, the thing is that pressure affects the "effective length" of the tube.
Let me explain, tubes are not as easy as strings. A string has a ...
- 8,244
21
votes
Accepted
Intuition behind the differential equation for forced oscillations
It's better to write the differential equation for forced oscillations in a different way that makes it more relatable to Newton's second law:
$$m\ddot{x}=F_0\sin{(\omega''t)}-b\dot{x}-kx$$
Now we can ...
- 416
20
votes
Accepted
Why does an acoustic guitar body amplify all notes and not just certain ones?
Every resonator amplifies just certain frequencies while it inhibits all others.
This is true only for very simple resonators. The shape of the guitar body is such that it has a different size at ...
- 12.3k
18
votes
Non-resonant but efficient frequencies
This is a subtle issue! Your intuition is correct (a driving at $f_0/2$ should be very effective) even though the graph seems to contradict this. The reason is that the graph displays the response to ...
- 98.6k
18
votes
Does amplitude really go to infinity in resonance?
It is instructive to analyze the problem in time domain. When the driving force is $F_0 \cos(\omega_0 t)$ and the mass is initially at rest at its equilibrium position, the solution is
$$x =\frac{F_0}{...
- 10.9k
15
votes
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 ...
- 1,709
14
votes
Accepted
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 (...
- 176k
13
votes
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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 ...
- 12.3k
13
votes
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 ...
- 131
12
votes
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 ...
- 7,494
11
votes
Accepted
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 ...
- 14.2k
11
votes
Accepted
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 ...
- 803
11
votes
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-...
- 4,805
10
votes
Accepted
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 $90^\circ$ ...
- 86.8k
10
votes
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 ...
- 1,297
10
votes
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 ...
- 201
10
votes
Accepted
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 ...
- 15.2k
10
votes
Accepted
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 ...
- 53.1k
10
votes
Does amplitude really go to infinity in resonance?
In the real world, the vibrational amplitude of an underdamped system driven at resonance does get big- up to the point at which the moving parts in the system bang into their limits, and then ...
- 83.7k
9
votes
Why do tall buildings have low resonant frequencies?
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 = ...
- 699
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