Physics of Musical Sound

Properties of traveling  waves

Waves

A disturbance that travels through space (usually through some medium).

Transverse-medium moves perpendicular to wave

-eg. water waves, light

Longitudinal-medium moves in same direction as wave

-eg. sound

Transient waves or impulses are of short duration and localised in space.

Periodic waves last a long time and are spread out in space.

Properties of traveling  waves

Speed, wavelength and frequency  related by v = f∙λ.

Reflection

-Wave hits an alteration in the medium and a portion of the energy bounces. Energy keeps same speed but is reversed in direction.

-Smooth surfaces produce specular reflection. Plane wave in produces plane wave out. Good for echoes.

-Rough surfaces (roughness > ) produce diffuse reflection. Plane waves in, random spherical waves out.

Properties of traveling  waves

Refraction

Bending of a wave at a place where  the velocity changes.

Occurs where go from one medium  to another.

Very important in light; lenses, prisms, etc.

Very rarely seen in sound. Only normal case is sound traveling  particularly well over a warm lake at  evening.

Properties of Waves

Superposition

When two waves meet they do not  interact at all. The disturbance from  two waves is exactly the sum of the  individual disturbances. That is, for a  sound wave, the total pressure P(x,t)  can be written in terms of the  individual pressures P1(x,t) and  P2(x,t)    P(x,t) = P1(x,t) + P2(x,t).

We call this Superposition  of the  waves and say that the relationship  is Linear .

Properties of Waves

Interference

If same wave travels to a place by two different paths then when the waves cross you get interference.

If waves line up perfectly then you get constructive interference and the resulting sound is louder than  either wave.

If one wave is l /2 behind the other  then the waves cancel and you get destructive interference. Result  softer than either.

Beats

If two waves with different frequencies f1 and f2  arrive at same place hear beats if frequencies are  close enough.

Beats are at difference frequency |f1-f2|.

Once frequencies get far enough apart hear a  musical interval.

Is a fuzzy region between!

Properties of Waves

Interference Problems

Plane surfaces in a concert hall give  rise to specular reflections that  interfere with direct sound to give  loud and soft spots in the hall.

We hear the effects of interference  as the production of beats  in the  sound. These are noticeable  loud/soft variations either in space  as you move your head or in time, if  sources have different frequencies.