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.

#. The wave is linear, i.e., assuming :math:`s(x, t)` is the transverse displacement:

   #. :math:`\frac{|s(x, t)|}{L} \ll 1`, where :math:`L` is the string length

   #. :math:`\left| \frac{\partial s}{\partial x} \right| \ll 1`

   #. the tension is constant thoughout the string

   #. the linear density is constant throughout the string

   #. the displacement must be orthogonal to the string's equilibrium shape

   #. no damping or energy dissipation within the string

**Links:**

#. `Physics LibreTexts, formula 16.5.1 <https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/16%3A_Waves/16.05%3A_Energy_and_Power_of_a_Wave>`__.

.. py:currentmodule:: symplyphysics.laws.waves.average_power_of_sinusoidal_wave_on_stretched_string

.. py:data:: wave_average_power

    Average :attr:`~symplyphysics.symbols.basic.power`, or rate of energy transfer, of the wave.

Symbol:
    :code:`P`

Latex:
    :math:`P`

Dimension:
    :code:`power`


.. py:data:: string_linear_density

    :attr:`~symplyphysics.symbols.basic.linear_density` of the string.

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`mass/length`


.. py:data:: phase_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.phase_speed` of the wave.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: wave_angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of the wave.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: wave_amplitude

    Amplitude of the wave. See :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance`.

Symbol:
    :code:`u_max`

Latex:
    :math:`u_\text{max}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`P = mu * v * w^2 * u_max^2 / 2`


    Latex:
        .. math::
            P = \frac{\mu v \omega^{2} u_\text{max}^{2}}{2}