Intensity of Sound

A sound wave is intense and loud if it has a large amplitude. However, the amplitude of a sound wave is hard to measure directly, and it is more convenient to reckon the intensity of a sound wave by the energy it carries. 

The intensity of a sound wave is defined as the energy per second transported by this wave per square meter of the wavefront, that is, the power transported by this wave per square meter. 

Thus, to measure the intensity, we have to erect an area facing the wave, and we have to check how much energy the wave delivers in this area per second. It can be shown that the intensity of a sound wave is proportional to the square of the pressure disturbance it produces in the air; equivalently, the intensity is proportional to the square of the density disturbance.

The unit of intensity is the watt per meter squared (W/m2). At a frequency of 1000 Hz, the minimum intensity audible to the human ear is about 2.5 × 10-12 W/m2. This intensity is called the threshold of hearing. There is no upper limit for the audible intensity of sound; however, intensity above 1 W/m2 produces a painful sensation in the ear.

Note that since the eardrum has an area of about 4 × 10-5 m2, the energy delivered per second by a sound wave of minimum intensity is only about 2.5 × 10-12 J/m2 × 4 × 10-5 m2 ≅ 10-16 J; this is a very small amount of energy, and it testifies to the extreme sensitivity of the ear.


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