Intensity of sound wave via displacement amplitude
==================================================

The intensity of a sound wave is the rate per unit area of energy transfer
through or onto a surface. It depends on the density of the medium, the phase
speed and the angular frequency of the wave and the amplitude of particles
in the medium.

**Links:**

#. Equation 17-27 on p. 489 of "Fundamentals of Physics" by David Halladay et al., 10th Ed.

.. py:currentmodule:: symplyphysics.laws.waves.intensity_of_sound_wave_via_displacement_amplitude

.. py:data:: wave_intensity

    :attr:`~symplyphysics.symbols.basic.intensity` of the sound wave.

Symbol:
    :code:`I`

Latex:
    :math:`I`

Dimension:
    :code:`power/area`


.. py:data:: medium_density

    :attr:`~symplyphysics.symbols.basic.density` of the medium in which the sound wave is being propagated.

Symbol:
    :code:`rho`

Latex:
    :math:`\rho`

Dimension:
    :code:`mass/volume`


.. 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:: angular_frequency

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

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: displacement_amplitude

    Displacement amplitude of the particles in the medium. See :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance`.

Symbol:
    :code:`s_max`

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

Dimension:
    :code:`length`


.. py:data:: law

    :code:`I = rho * v * w^2 * s_max^2 / 2`


    Latex:
        .. math::
            I = \frac{\rho v \omega^{2} s_\text{max}^{2}}{2}