# 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.