# Tag Info

16

Usually, the (sinusoidal) driven harmonic oscillator is damped, and the first two parts of your solution (which depend on the initial conditions, while the third term does not) are transient, i.e. not relevant after a short time. That the solution $$x(t) = \frac{F_0\sin(\omega t)}{m(\omega_0^2 - \omega^2)}$$ cannot be the "full" solution to the equation of ...

10

When you pluck a string or hit a drum or sound a not on a flute, the instrument and the air in and around it vibrate and this vibration propagates as sound waves in the air to your hear drum. When you hear an instrument being played, what you recognise as the note is the base frequency. 'C' corresponds to $261.6$ Hz and is the same for a piano or a guitar. ...

4

Clearly the motion of the mass can not be described by a single sine! What's going on here? The general solution to the simple harmonic oscillator is the sum of the unforced response (homogeneous solution) and the forced response. The homogeneous solution is $$x_h(t) = x_h(0) \cos(\omega_0 t) + \frac{\dot x_h(0)}{\omega_0}\sin(\omega_0 t)$$ Thus, ...

3

There is a technique called flageolet where you damp the string with a finger laid lightly onto the site at the node of a higher harmonic. You do not press the string to the fretboard but just damp the string at a position, where there is a node of the specific harmonic. When you now pluck the string all harmonics, which do not have a node at the specified ...

3

Pitch, in music, is equivalent to frequency. How often the wavefore cycles. This is usually defined by length, i.e. how long the string is, how long the pipe is, etc. It can also be affected by the tension (how tight the string is.) Timbre, the sound of a specific instrument, is defined by the "shape" of the wavefore, whether spikes, round, square, or ...

3

A few observations. First - if you record sound for a short time, the bandwidth of the sample will result in a smearing of the peaks. This only really matters if the sample is very short - with a 1 second sample you would have 1 Hz resolution, but if you sample for 0.01 second, the bandwidth is 100 Hz. Second, you are using a scale that is quite compressed ...

2

Sound waves are made of alternation of compression (higher density) and rarefaction (lower density) regions in the air. However, this can be somewhat difficult to visualize. Because of this, textbooks often show the wave like it's a string in the organ pipe. Really what the curves are showing you in the amplitude of this compression wave. It's also drawn ...

2

Consider the following diagram: A U tube contains a fluid with higher level in the right hand side. This could be achieved as you suggested or more simply by applying a partial vacuum on the right hand side: the higher (atmospheric) pressure in the left tube then pushes the fluid up into the right side, until a level difference of $y$ is achieved. At ...

2

Edit after providing the plot: Please note, that the simple model prediction of harmonics frequency position does not say anything about its strength in actual sound. It is typical feature of brass instruments in middle and lower registers that the fundamental frequency is not the strongest. Original answer: I am sorry guys, but that's well-known and ...

2

Yes, it most certainly can. It's much easier to visualize if you consider a length of flexible steel or plastic. You can shake it a bit, then toss it in the air so it's not constrained, and it will (if properly initiated) vibrate at a resonant wavelength. I think the confusion most people will get from your question is that everyday string is "floppy," ...

2

For your example of a violin string, you can immediately determine that it is not simple harmonic motion by listening to it. Simple harmonic motion is a pure tone of a single frequency. Violins don't sound like that so you immediately know there are harmonics and it therefore is not a simple harmonic oscillator. As some other people have mentioned, a tuning ...

1

The pure simple harmonic motion is in real life very very rare. There are some cases which are really close (e.g. for engineering purposes). That might be: Small-amplitude oscillation of a mass on a spring (small enough for spring nonlinearities not to be pronounced) or other kinds of these simple or moreless model oscillators. Tuning fork. Strictly ...

1

A "standing wave" is not a real wave - it is simply our observing the superposition of two waves - one traveling to the left and one traveling to the right. If they have the same amplitude and propagate at the same velocity there will be stationary points on the string. This is true regardless of whether the ends of the string are "open" or "closed". ...

1

Imagine a little wheel spinning on the rim of a big wheel. The resulting motion of a point on the little wheel is a combination of different simple harmonic motions. Think $$x = A\sin(\omega_1 t + \phi_1) + B \sin(\omega_2 t + \phi_2)$$ Depending on the relative frequencies and phases, the max amplitude can be $A+B$; the kinetic energy is just $\frac12 m ... 1 The answer of Gert is very insightful, but there is a slight error in the equation of motion. (Sorry, since I am new here, I cannot comment yet, therefore I have to write it as a separate answer.) Instead of$y$the variable should by$x$, which measures the height of the column from the equilibrium position (when the water levels are equal in both ... 1 The answer I gave above is actually only approximately correct, if the radius of the circular bend is large compared to the radius of the U tube. The reason is that in the bent section the fluid actually rotates around its centre point, not translates as previously assumed. Look at the diagram below: Firstly let's define a few things: Total length of the ... 1 These curves show acoustic displacement or acoustic velocity. For acoustic pressure they would be "inverted" (nodes at the open end, antinodes at the closed end). In presented 1D case are all of them actually scalars (or can be treated as such). The curves show just the magnitude. I know, these graphics are confusing. Nowadays it could be easily done by ... 1 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$90^\circ$out of phase with one another. Note that at a compression$C\$ where the pressure is a maximum the displacement of the particle is zero and the same is true ...

1

I was just researching this kind of questions, since the derivation found in most textbooks, in terms of tension, seems a little unrelated to material properties. Three things: As pointed out, the tension T needs to be inside the square root The velocity of sound in the string material is unrelated to the (phase) velocity of the wave. As the formula shows, ...

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