# Physics of Musical Sound

# Properties of traveling Â 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 Â waves

Speed, wavelength and frequency Â related by v = fâˆ™Î».

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 Â waves

Refraction

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

Occurs where go from one medium Â to another.

Very important in light; lenses, prisms, etc.

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

## Properties of Waves

Superposition

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

We call this Superposition Â of the Â waves and say that the relationship Â 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 Â either wave.

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

## Beats

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

Beats are at difference frequency |f1-f2|.

Once frequencies get far enough apart hear a Â musical interval.

Is a fuzzy region between!

## Properties of Waves

Interference Problems

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

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

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