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  • Define intensity, sound intensity, and sound pressure level.
  • Calculate sound intensity levels in decibels (dB).
Photograph of a road jammed with traffic of all types of vehicles.
Noise on crowded roadways like this one in Delhi makes it hard to hear others unless they shout. (credit: Lingaraj G J, Flickr)

In a quiet forest, you can sometimes hear a single leaf fall to the ground. After settling into bed, you may hear your blood pulsing through your ears. But when a passing motorist has his stereo turned up, you cannot even hear what the person next to you in your car is saying. We are all very familiar with the loudness of sounds and aware that they are related to how energetically the source is vibrating. In cartoons depicting a screaming person (or an animal making a loud noise), the cartoonist often shows an open mouth with a vibrating uvula, the hanging tissue at the back of the mouth, to suggest a loud sound coming from the throat [link] . High noise exposure is hazardous to hearing, and it is common for musicians to have hearing losses that are sufficiently severe that they interfere with the musicians’ abilities to perform. The relevant physical quantity is sound intensity, a concept that is valid for all sounds whether or not they are in the audible range.

Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity     I size 12{I} {} is

I = P A , size 12{I= { {P} over {A} } } {}

where P size 12{P} {} is the power through an area A size 12{A} {} . The SI unit for I size 12{I} {} is W/m 2 . The intensity of a sound wave is related to its amplitude squared by the following relationship:

I = ( Δ p ) 2 2 ρv w . size 12{I= { { left (Δp right )} over {2 ital "pv" size 8{m}} } rSup {2} } {}

Here Δ p is the pressure variation or pressure amplitude (half the difference between the maximum and minimum pressure in the sound wave) in units of pascals (Pa) or N/m 2 . (We are using a lower case p for pressure to distinguish it from power, denoted by P above.) The energy (as kinetic energy mv 2 2 ) of an oscillating element of air due to a traveling sound wave is proportional to its amplitude squared. In this equation, ρ is the density of the material in which the sound wave travels, in units of kg/m 3 , and v w is the speed of sound in the medium, in units of m/s. The pressure variation is proportional to the amplitude of the oscillation, and so I size 12{I} {} varies as ( Δ p ) 2 size 12{ \( Λp \) rSup { size 8{2} } } {} ( [link] ). This relationship is consistent with the fact that the sound wave is produced by some vibration; the greater its pressure amplitude, the more the air is compressed in the sound it creates.

The image shows two graphs, with a bird positioned to the left of each one. The first graph represents a low frequency sound of a bird. The pressure variation shows small amplitude maxima and minima, represented by a sine curve of gauge pressure versus position with a small amplitude. The second graph represents a high frequency sound of a screaming bird. The pressure variation shows large amplitude maxima and minima, represented by a sine curve of gauge pressure versus position with a large amplitude.
Graphs of the gauge pressures in two sound waves of different intensities. The more intense sound is produced by a source that has larger-amplitude oscillations and has greater pressure maxima and minima. Because pressures are higher in the greater-intensity sound, it can exert larger forces on the objects it encounters.

Sound intensity levels are quoted in decibels (dB) much more often than sound intensities in watts per meter squared. Decibels are the unit of choice in the scientific literature as well as in the popular media. The reasons for this choice of units are related to how we perceive sounds. How our ears perceive sound can be more accurately described by the logarithm of the intensity rather than directly to the intensity. The sound intensity level     β size 12{β} {} in decibels of a sound having an intensity I in watts per meter squared is defined to be

Questions & Answers

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Practice Key Terms 3

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