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phys: fix standing wave equations

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eggy 2020-12-14 10:51:19 -05:00
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docs/sph3u7.md
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@ -668,11 +668,8 @@ The locations of zero amplitude are called **nodes** and the locations of maximu
<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:
$$
\lambda_n=\frac{2}{n}L \\
f_n=\frac{nv}{2L}
$$
In a stretched string or a **half-open** air column, 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, where $L$ is the string length:
$$\lambda_n=\frac{2}{n}L$$
Inside an **air column**, the difference in pressure allows for the formation of standing waves as waves reflect off of the interface where air changes pressure. A closed end must have nodes while open ends must have antinodes.
@ -680,6 +677,9 @@ Inside an **air column**, the difference in pressure allows for the formation of
Resonance occurs in an air column when the length of the open tube is a multiple of half the wavelength of the sound. **Resonant lengths** occur at each antinode.
In a **open-ended** or **closed-ended** air column:
$$\lambda_n=\frac{n}{4}L$$
## 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).