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If the wave is truly monochromatic then it will be sinusoidal. If it has a different profile then Fourier's theorem tells us that it can be built from an infinite series of (co)sine waves with increasing integer harmonics of the principle frequency (i.e. not monochromatic).

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The electromagnetic field in absence of charges and current is described by a wave equation. The solutions of the wave equations in a general setting (without symmetry contestants and without boundary conditions) are plane waves with a fixed frequency and momentum. These are purely sinusoidal $\propto \sin(k x-\omega t)$. Similarly, sound waves are the ...

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A plane wave is a single frequency , a sinusoidal variation in space and time by mathematical construction. Mathematically : the traveling wave solution to the wave equation ... is valid for any values of the wave parameters, and since any superposition of solutions is also a solution, then one can construct a wave packet solution as a sum of ...

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The papers described in the report you've linked to demonstrate examples of sound amplification by spontaneous emission. This is independent of the characteristics of the waves that those source produce. As it happens, for sound (as opposed to light) it is relatively easy to create waves that have high spatial coherence and well-defined wave vectors $\vec k$...

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No. To create a sonic boom, a plane needs to be travelling at greater than the speed of sound in the medium the sound travels in, namely the air. Speed relative to other planes or relative to the ground doesn't matter. Only speed relative to the air that it is moving through.

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There are nonlinear systems that present a sub-harmonic response. That is, a harmonic with a frequency lower than the excitation frequency. For example, a spring with a cubic nonlinearity can present this type of behavior. There are also systems that present multi-stability, where you have different stable configurations with different values of energy (see ...

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The following experiment will shine light on this. What is happening here? The string has fixed boundary conditions but the left side of the string is driven by a small amplitude oscillation. The driving frequency of each string increases as you go down. The first and last string both are driven by a resonant frequency. Recall that $f=c/\lambda$ with $c$ ...

2

the maximum possible accuracy of any sound-based imaging scheme depends on the wavelength of the sound relative to the size of the things you wish to detect with it. This is because an object is poorly-coupled to a sound wave if its dimensions are less than the wavelength of the sound. High spatial resolution for imaging or distance measurement hence ...

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yes, you will. In a sound wave that strikes the bottle wall, part of it will bounce off and away from the bottle and part of it will be transmitted through the wall, and you'll hear it inside. The thicker the wall, the more will bounce off and less will be transmitted.

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The beat frequency, mathematically, is indeed $\frac{f - f_0}{2}$, as can easily be shown using the factor formula in trigonometry. However, the perceived beat frequency is twice of that, which is $f - f_0$. This is because the beat frequency modulates the amplitude of the sound wave. In one full cycle of $2\pi$, the amplitude goes both positive and negative,...

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The general problem of speaker enclosure isolation is one of deliberately creating an impedance mismatch between the bottom of the speaker and the floor upon which it sits. The most effective approach is to use the speaker enclosure's own mass in combination with a springy support to prevent the transmission of sound above a certain cutoff frequency which in ...

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Actually, you've gotten the issue backwards! You complain that the Fourier series is illegitimate because we don't have an "actual" periodic function, so we repeat the function by "brute force". But that's not the right way to look at it. The Fourier series properly represents functions defined on the circle, i.e. functions $f(x)$ for $x \in [0, a]$ with $... 1 The note produced by vibrating air in the instrument. Blowing air over the player's lips is what sets up the vibration. You can do this without an instrument. The instrument has a resonance frequency. Vibrations at that frequency get reinforced. The oscillating pressure acts on the lips and encourages them to vibrate at the resonance frequency. This makes ... 1 Now if we think that sound wave is like an object and use relative motion than sound will approach wall with speed$v + v_{s}\$... No, I think you are misunderstanding something here. A linear sound wave will always propagate at the speed of sound once emitted in a homogeneous, uniform medium. If your expression were correct, how could a shock wave form? ...

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A signal can indeed propagate through a body faster than the speed of sound; that's what you call a shock wave. Therefore, if the buoyancy force causes the particles at the bottom of an object to acquire a speed larger than that of sound, a shock wave will be generated and will propagate upwards through the object. The propagation speed of the shock is ...

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High buoyancy and low speed of sound have conflicting requirements. A low molecular weight increases buoyancy but it also increases the speed of sound at a given temperature. Similarly, for a gas a at least, high temperature increases buoyancy but it also increases the speed of sound. How about a liquid or solid at very low temperature? The mere act of ...

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I was wondering if it is possible for an object of a certain material to be put in a buoyant medium in such a way that the buoyant force (caused by the pressure difference “above” and “below” said object and by the interactions with molecules of the medium under that regime) creates an acceleration that causes a motion that exceeds the sound speed of the ...

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Essentially, yes. Anytime sound passes from one substance into a substance in which the speed of sound is different, some energy will be reflected and some refracted. But, the amount reflected is simply based on the ratio between the speeds of sound in those media. So it doesn't matter too much whether it's going from a faster medium to a slower medium or ...

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