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Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area (i.e., surface power density ).
The energy and power of a wave are proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave. Intensity is defined as the power divided by the area. …
Calculate the intensity and the power of rays and waves. All waves carry energy. The energy of some waves can be directly observed. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls. Loud sounds pulverize nerve cells in the inner ear, causing permanent hearing loss.
It is of interest to know how “concentrated” the power is in any region. Therefore, we define a property called intensity of the wave by dividing power by the area of the surface the wave is flowing through, here it will be \(A_\perp\text{.}\)
By definition, the intensity (I) of any wave is the time-averaged power ( P ) it transfers per area (A) through some region of space. The traditional way to indicate the time-averaged value of a varying quantity is to enclose it in angle brackets ( ).
The time average of the energy flux is the intensity \(I\) of the electromagnetic wave and is the power per unit area. It can be expressed by averaging the cosine function in Equation \ref{16.29} over one complete cycle, which is the same as time-averaging over many cycles (here, \(T\) is one period):
Sound intensity. The intensity of sound is the power per unit area, or. I = P / [area] (we just used A for amplitude) The human ear can tolerate sound intensities as high as ~ 1 W/m2, and can detect as low as 10-12 W/m2.
