The psychological magnitude loudness is associated with a given SPL. Judgements of whether two sine tones sound equally loud show fairly low dispersion among different individuals. Judgements on "how much" louder one tone is than another require previous conditioning or training and yield results that fluctuate greatly from individual to individual and from occasion to occasion.

Curves of Equal Loudness

Tones of the same SPL but with different frequencies are in general judged as having different loudness. SPL is thus not a good measure of loudness, if we inter compare tones of different frequency. Experiments have been performed to establish curves of equal loudness, taking the SPL at 1 KHz as a reference quantity. These are shown below

Fletcher and Munson curves

pressure =
or Force = difference in pressures times surface area F = (p-p')S
W = Fx = (mv)/2 . Unit is newtons/metre = Joule
W = work done, F = force, x = distance travelled , m = mass, v = velocity

The velocity of transverse elastic waves is given by:

where d = "linear density" of the medium i.e. mass per unit length (in kg/m) Thus, then more tense a string is faster the transverse wave will travel ( higher frequency). On the other hand, the more dense it is, the slower the waves will propagate.

For longitudinal waves the propagation speed in a medium of density (in kg/m3) and where the pressure is p (in Newton/m) is given by:

For an ideal gas the ratio p/ is proportional to the "absolute" temperature. Although air is not 100% ideal it behaves approximately so, and the velocity of sound waves may be expressed as

P = mechanical power. Units are Joule/sec called Watt