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phys: add standing waves

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eggy 2020-12-07 20:28:43 -05:00
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@ -655,6 +655,22 @@ As a wavefront passes an aperture, there are fewer points beside it and the wave
For observable diffraction, the wavelength must be greater than or equal to the width of the aperture. For observable diffraction, the wavelength must be greater than or equal to the width of the aperture.
## 4.4 - Standing waves
A standing wave does not travel, so no energy is transferred. They are caused by the interference of symmetrical travelling waves moving in opposite directions.
<img src="/resources/images/standing-wave.gif" width=700></img>
The locations of zero amplitude are called **nodes** and the locations of maximum amplitude are **anti-nodes**. Adjacent nodes are separated by $\frac{\lambda}{2}$. The wave speed is determined by the medium and the wavelengths of standing waves that fit on the medium are determined by the length of the medium.
<img src="/resources/images/harmonic-waves.png" width=700>(Source: Kognity)</img>
In a stretched string, the frequencies that would produce standing waves are known as **natural frequencies**, and are individually known as **harmonics** The image above shows the first four harmonics. The first harmonic is also known as the **fundamental frequency**. The wavelength and frequency of the $n$th harmonic is equal to, here $L$ is the string length:
$$
\lambda_n=\frac{2}{n}L \\
f_n=\frac{nv}{2L}
$$
## 6.1 - Circular motion ## 6.1 - Circular motion
Circular motion is any motion along a circular path. The instantaneous velocity of an object in circular motion at any point is always tangent to its point on the circle, so the difference between any two velocities ($\Delta \vec{v}$) is radial (lies along the radius). Circular motion is any motion along a circular path. The instantaneous velocity of an object in circular motion at any point is always tangent to its point on the circle, so the difference between any two velocities ($\Delta \vec{v}$) is radial (lies along the radius).