SOUND

SPEED OF A WAVE ON A STRINGWhat affects the speed of a wave on a string?

The properties of the medium through which the wave travels determine the speed of the wave.

If the medium changes, the speed of the wave changes.

SPEED OF A WAVE ON A STRINGAs the wave move to the right, each particle (red dot) is displaced, one after the other, from its equilibrium position.

Particle 1 pulls particle 2 upwards.

Particle 2 pulls particle 3 upwards, etc.

SPEED OF A WAVE ON A STRINGThe speed of the wave depends on

how quickly one particle of the string is accelerated by the force exerted on it by a neighboring particle.

According to Newton’s 2nd Law, it would make sense that a stronger net F would give a larger acceleration, and thus a faster moving wave.

SPEED OF A WAVE ON A STRINGThe greater the Tension in the string, the greater the pulling force the particles exert on each other.

A smaller mass will accelerate more quickly (less inertia), so a wave will travel faster on a string whose particles have a small mass.

SPEED OF A WAVE ON A STRING

Where F is the tension in the string

m/L is the linear density (mass per unit length) of the string

EXAMPLETransverse waves travel on

each string of an electric guitar after the string is plucked. The length of each string is 0.628m, and the mass is 0.208g for the highest pitched E string and 3.32 g for the lowest pitched E. Each string is under a tension of 226N. Find the speed of the waves on the two strings.826 m/s and 207 m/s

EXAMPLEOne end of each of two identical

strings is attached to a wall. Each string is being pulled equally tight by someone at the other end. A transverse pulse is sent traveling along string A. A bit later an identical pulse is sent traveling along string B. What, if anything, can be done to make the pulse on string B catch up with and pass the pulse on string A?826 m/s and 207 m/s

THE NATURE OF SOUNDSound is a longitudinal wave that is

created by a vibrating object (ex. Guitar string, vocal cords, diaphragm of a loudspeaker)

Sound can be created or transmitted only in a medium – a solid, liquid, or gas

Demo – bell jar

THE NATURE OF SOUNDWhen the diaphragm of a

loudspeaker moves outward, it compresses the air directly in front of it.

It causes the air pressure to rise slightly, and this region is called a condensation

THE NATURE OF SOUNDThe condensation moves away from

the speak at the speed of sound.

THE NATURE OF SOUNDAfter producing a condensation, the

speaker reverses its motion and moves inward, producing a rarefaction

The air pressure is slightly less than normal

THE NATURE OF SOUNDAs the wave passes,

the air molecules are pushed and pulled about their equilibrium position (simple harmonic motion)

The wavelength of the wave is the distance between 2 successive condensations or rarefactions.

THE NATURE OF SOUNDA sound wave spreads out

in space after it is produced by the speaker

Remember, the air molecules vibrate around their equilibrium position as the wave is passing, colliding with their neighbor passing the rarefactions and condensations forward and return to their equilibrium position

THE NATURE OF SOUNDWhen the

condensations and rarefactions arrive at the ear, they force the eardrum to vibrate at the same frequency as the speaker diaphragm

Each cycle of a sound wave includes one condensation and one rarefaction

THE NATURE OF SOUNDA sound wave traveling

in a tube consists of a series of alternating condensations and rarefactions.

The air pressure in the tube varies sinusoidally

A Ruben’s Tube uses gas and a flame to “show” a pattern of different flame heights which represent the sound being played