All Questions
29 questions
0
votes
1
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77
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How is a resonant bandpass filter similar/different from a damped mass-spring oscillator? They seem to behave both similar and different in testing
Background
I am using resonant bandpass filters as musical oscillators. One can excite an array of them at harmonic frequencies and given Q values for a note by, for example, running a burst of noise ...
- 343
13
votes
3
answers
4k
views
Why do strings in musical instruments have helical shape?
We learn that waves travels in strings under tension, have fundamental frequencies, but I have no luck understanding why don't musical instruments have simple strings with uniform thickness which we ...
- 169
1
vote
1
answer
189
views
How to test resonance frequency of spring using sound?
I've done experiment with spring and mass to determine the natural frequencies of 4 springs. The first experiment went well but I had some problem when I want to test the resonant frequency. I'll ...
- 23
2
votes
1
answer
142
views
"Spherical wave" in a 2D square lattice of masses and springs
Assume a 2D square array of masses with mass $m$ connected by springs with constant $\kappa$. Then the equation of motion for small perturbations in the plane of the array to the mass at $(l,n)$ is
$$
...
- 990
1
vote
1
answer
457
views
Does Hooke's law explain classical wave behavior?
Will Hooke's law $F = -kx$ applied to a large mass-spring grid array such as:
provide the full and complete mechanistic explanation for classical wave behavior, including the 2nd order wave ...
- 627
0
votes
1
answer
52
views
Balance equation for a string-spring system: meaning of 2nd Newton's law for massless objects $m=0$ [closed]
The usual homogeneous one dimensional wave equation for transverse (vertical) vibrations is given by
$$u_{tt}-a^2u_{xx}=0,\qquad a=\sqrt{T/\rho}$$
where $u=u(x,t)$ is the vertical displacement, $T$ is ...
- 111
0
votes
0
answers
266
views
Mechanics of an (infinite small) spring oscillator
I've been thinking about creating a continuous rope, made out of infinitely many springs, with infinitely small distances between them.
At first, I developed the Euler-Lagrange Equations:
$$
\mathcal{...
- 1,843
2
votes
1
answer
101
views
Why doesn't a compression pulse on a spring move backwards?
I've a spring and I give it a single impulse towards left. A compression zone is produced as is shown in the picture, then this compression moves ahead to the left of the spring and we see a ...
- 1,380
2
votes
0
answers
2k
views
How do tension and linear density affect speed of waves in spring? (Qualitative)
Wave speed, tension and linear density (mass per unit length) can be related by the following equation:
$$v=\sqrt{\frac{T}{\mu}}$$
The derivation of the equation could be done by using calculus.
I ...
- 273
4
votes
3
answers
1k
views
Longitudinal Wave meets Transverse
Okay, so the title may seem like a YouTube viral, but yes, my friend asked me this question today:
What if a longitudinal wave superposes a transverse wave? Is it possible? What would happen then?
I ...
- 81
0
votes
1
answer
342
views
Why is the phase velocity of waves on a rope independent of the wave length?
A rope is described by the wave equation
$$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$
It is well known that there is no dispersion for resulting wave solutions. This implies that all plane waves ...
- 10.4k
4
votes
4
answers
1k
views
Why does the phase velocity of a string attached to springs depend on the wave length?
A string can be described by the wave equation
$$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$
while a string attached to a spring (i.e. with a harmonic restoring force) at each location is ...
- 10.4k
12
votes
4
answers
3k
views
Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines?
The defining property of SHM (simple harmonic motion) is that the force experienced at any value of displacement from the mean position is directly proportional to it and is directed towards the mean ...
- 1,123
9
votes
1
answer
452
views
Motivating classical wave equation PDE
I'm teaching a geometry course covering spectral problems, using eigenvalues of the Laplace operator for shape analysis ("Can you hear the shape of a drum?"). I thought I'd cover where the wave ...
- 325
1
vote
1
answer
24k
views
Finding the Amplitude of a Spring Oscillation given initial Position and Velocity [closed]
I'm trying to create a physics simulation, and I need to be able to determine the amplitude of the oscillation of a mass-and-spring system given any position that the mass might be in and the velocity ...
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