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This topic is contained in pages $133-139$ of the textbook.
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All waves transfer energy.
The following relationship can be used to solve problems involving the energy transferred by a wave and its amplitude.
$$ E=kA^2 $$
→ $\frac{E_1}{A_1^2}=\frac{E_2}{A_2^2}$
The following relationships can be used to solve problems involving wave motion, phase difference or phase angle ($\phi$, measured in radians), and separation ($x$, in $m$).
$$ y=Asin2\pi (ft - \dfrac{x}{\lambda}) $$
→ $y=Asin2\pi (ft + \dfrac{x}{\lambda})$ for reflected waves.
$$ \phi = \dfrac{2\pi x}{\lambda} $$
| Phase Difference | Separation of Points |
|---|---|
| 0 | 0 |
| $\frac{\pi}{2}$ | $\frac{\lambda}{4}$ |
| $\pi$ | $\frac{\lambda}{2}$ |
| $2\pi$ | $\lambda$ |
Stationary waves are formed by the interference of two waves, of the same frequency and amplitude, travelling in opposite directions.
→ Incident and reflected waves interfere to form maxima and minima.
A stationary wave can be described in terms of nodes and antinodes.
→ nothing and nodes
The general formula for the frequency of a wave’s $n^{th}$ harmonic is $f_n=n\times f_1$, where $f_1$ is the fundamental frequency ($f_1=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$).