Key Equations
Wave Types, Polarisation & Stationary Waves — AQA A-Level Physics
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First harmonic frequency
$$f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$
- Where:
- $f$ = fundamental frequency (Hz)
- $L$ = vibrating string length (m)
- $T$ = tension (N)
- $\mu$ = mass per unit length (kg \(m^{-1}\))
Derived from v = f lambda with lambda = 2L and v = sqrt(T/mu). L is the distance between fixed points.
Wave speed on a string
$$v = \sqrt{\frac{T}{\mu}}$$
- Where:
- $v$ = wave speed (m \(s^{-1}\))
- $T$ = tension (N)
- $\mu$ = mass per unit length (kg \(m^{-1}\))
Used to verify wave speed from the stationary waves practical.
Harmonic frequencies
$$\begin{aligned}
f_n &= nf_1 \\
&= \frac{nv}{2L}
\end{aligned}$$
- Where:
- $f_n$ = frequency of the nth harmonic (Hz)
- $n$ = harmonic number (1, 2, 3...)
- $f_1$ = fundamental frequency (Hz)
- $v$ = wave speed (m \(s^{-1}\))
- $L$ = string length (m)
Each harmonic is an integer multiple of the fundamental. The nth harmonic has n antinodes and (n+1) nodes.