Characteristics of Sound Waves

Transverse and Longitudinal Waves Classification

of waves is according to the direction of

propagation. In transverse waves the particles

vibrate perpendicular to the direction of

propagation (for example, a vibrating string or a

water wave) In longitudinal waves the particles

vibrate in the direction of propagation (for

example, an oscillating spring or sound waves)

The subject of sound is known in physics as

acoustics. One differentiates sound according to

the frequency as infrasonic, audible sound,

ultrasonic and hypersonic. Sonic infrasound is a

sound too low for humans to hear, below 20 Hertz.

Ultrasound is a sound too high for humans to

hear, above 20,000 Hertz.

We can obtain an equation of motion (a "wave

equation") for a particle on a stretched string

by applying Fma to a little piece of string.

When we do this, we find that a solution is any

function whose argument is x vt or x - vt. The

exact nature of the function f(x - vt) depends on

how the string is wiggled. When the end of a

string is wiggled like a harmonic oscillator, the

transverse displacement of the string is given by

air pressure

time

longitudinal wave

Speed of Sound A sound wave can be represented by

placing a long coiled spring on a horizontal

table. If one moves the end back and forth

harmonically, regions of compression and

rarefaction travel along the spring. The speed of

sound accounts for these changes in pressure and

can be written as an equation depending on its

elastic characteristics.

For which B is the bulk modulus and is the

mass density of the medium in which the sound is

propagating.

Problems 1.) For steel the bulk modulus is

60?GPa and its density is 8 kgm-3. ?What is the

speed of sound in steel? Solution

2.) A wave is described as where

k 2.14 rad/m and ! 3.6 rad/s. Determine the

amplitude, wavelength, frequency, and speed of

the wave. Solution The amplitude is given. It is

2.10 cm. The wavelength is The frequency f is

The speed is

Superposition of Waves If wave displacements

are added together the resulting wave can show

either constructive or destructive interference.

If two waves of the same velocity and

wave- lengths are travelling in the same

direction, they will interfere. If they are in

phase they interfere constructively and result

in a stronger wave. If they are out of phase

and have the same amplitude, they cancel each

other out (destructive interference ).

Superposition of Waves

Two waves of the same phase

Two waves with equal but opposite phase

Constructive Interference

Destructive Interference

Standing Waves A standing wave is the result of

two waves of the same frequency and amplitude

moving in opposite directions to each other. A

mechanical example is a string that one wiggles

up and down and produces a propagating wave. If

one end is fixed, the wave will be reflected. As

a result, one cant observe a propagating wave

and instead the string experiences an oscillation

in one place. The antinodes will remain fixed and

the nodes will oscillate with a larger amplitude.

The distance between two nodes or antinodes is

the half wavelength of the original wave. Thus

for nodes we have the equation

Nodes The distance L of a crest from the center

is a half multiple of the wavelength.

with n 1, 2, 3 ...

Antinodes The distance L of a node from the

center is a multiple of the wave length plus a

quarter

with n 1, 2, 3 ...

Harmonics of Standing Waves

1st Harmonic

2nd Harmonic

3rd Harmonic

Beats If two travellng waves have slightly

different frequencies, they interfere and produce

a phenomen called beats.

The Doppler Effect The doppler effect

is the change in perceived or measured frequency

as the observer and the source travel relative to

one another of any kind of wave.

If the observer and the source move towards each

other, the frequency perceived by the observer

increases, if they move apart the frequency

decreases. For example, the sound of an ambulance

gets higher as it gets nearer and the tone gets

lower as it moves away. Observer at rest and

source of the signal moves Observer moves and

source of the signal at rest. The spacing of the

crests of the waves coming towards you is