On average, half the energy in a simple harmonic oscillator is kinetic and half is elastic. Little masses connected to other little masses with little springs as far as the eye can see. Mechanical waves in a continuous medium can be thought of as an infinite collection of infinitesimal coupled harmonic oscillators. Since kinetic and elastic energies are always positive we can split the time-averaged portion up into two parts. Replace power with energy (both kinetic and elastic) over time (one period, for convenience sake). If you don't care to see the sausage being made below, jump to the equation just before the vibrant table. This can be shown with a long, horrible, calculation. ⎡įor simple mechanical waves like sound, intensity is related to the density of the medium and the speed, frequency, and amplitude of the wave. The SI unit of power is the watt, the SI unit of area is the square meter, so the SI unit of intensity is the watt per square meter - a unit that has no special name.

That gives us an equation that looks like this… I = These look similar to the greater than and less than symbols but they are taller and less pointy. The traditional way to indicate the time-averaged value of a varying quantity is to enclose it in angle brackets ( ⟨⟩). Loudness will be dealt with at the end of this section, after the term level and its unit the decibel have been defined.īy definition, the intensity ( I) of any wave is the time-averaged power ( ⟨ P⟩) it transfers per area ( A) through some region of space. Use 'low' to describe sounds that are low in frequency. The word 'low' is sometimes also used to mean quiet, but this should be avoided. Sound waves with small amplitudes are said to be 'quiet' or 'soft'.

Sound waves with large amplitudes are said to be 'loud'. As a general rule the larger the amplitude, the greater the intensity, the louder the sound. It is a subjective quality associated with a wave and is a bit more complex. Loudness is a perceptual response to the physical property of intensity. It is an objective quantity associated with a wave. The intensity of a sound wave is a combination of its rate and density of energy transfer. When done by a neuronal circuit (like the circuits in your brain that connect to your ears) the resulting sensation is called loudness. When done by an electronic circuit (like the circuits in a telephone that connect to a microphone) the resulting value is called intensity. Instead, amplitude measurements are almost always used as the raw data in some computation. In any case, the results of such measurements are rarely ever reported. All types of amplitudes are equally valid for describing sound waves mathematically, but pressure amplitudes are the one we humans have the closest connection to. Humans have also been doing it electromechanically for about a hundred years with devices called microphones. Animals (including humans) have been doing it for several hundred million years with devices called ears. Pressure fluctuations caused by sound waves are much easier to measure. There are some optical techniques that make it possible to image the intense compressions are rarefactions associated with shock waves in air, but these are not the kinds of sounds we deal with in our everyday lives.

The period of a sound wave is typically measured in milliseconds. For typical sound waves, the maximum displacement of the molecules in the air is only a hundred or a thousand times larger than the molecules themselves - and what technologies are there for tracking individual molecules anyway? The velocity and acceleration changes caused by a sound wave are equally hard to measure in the particles that make up the medium.ĭensity fluctuations are minuscule and short lived. Measuring displacement might as well be impossible. The density amplitude is the maximum change in density.The pressure amplitude is the maximum change in pressure (the maximum gauge pressure).

Amplitudes associated with changes in bulk properties of arbitrarily small regions of the medium.The acceleration amplitude is the maximum change in acceleration.The velocity amplitude is the maximum change in velocity.The displacement amplitude is the maximum change in position.Amplitudes associated with changes in kinematic quantities of the particles that make up the medium.The amplitude of a sound wave can be quantified in several ways, all of which are a measure of the maximum change in a quantity that occurs when the wave is propagating through some region of a medium.

Average intensity of light equation