Average power of sinusoidal wave on stretched string¶

The average power of a wave of any type is proportional to the square of its amplitude and to the square of its angular frequency.

Conditions:

The wave is sinusoidal.

Links:

Physics LibreTexts, formula 16.5.1.

wave_average_power¶

Average power, or rate of energy transfer, of the wave.

Symbol:: P
Latex:: \(P\)
Dimension:: power

string_linear_density¶

linear_density of the string.

Symbol:: mu
Latex:: \(\mu\)
Dimension:: mass/length

phase_speed¶

phase_speed of the wave.

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

wave_angular_frequency¶

angular_frequency of the wave.

Symbol:: w
Latex:: \(\omega\)
Dimension:: angle/time

wave_amplitude¶

Amplitude of the wave. See euclidean_distance.

Symbol:: u_max
Latex:: \(u_\text{max}\)
Dimension:: length

law¶

P = 1/2 * mu * v * w^2 * u_max^2

Latex:: \[P = \frac{1}{2} \mu v \omega^2 u_\text{max}^2\]