A powerpoint explaining what sound waves are, the equation used to calculate displacement, the equation used to calculate pressure and the equation for intensity.

1. Sound Waves
Physics 101
http://www.passmyexams.co.uk/GCSE/
physics/images/long_waves.jpg

2. Properties of
Sound Waves
They propagate in three dimensions
as opposed to the one dimensional
waves we learned about previously
They cause the molecules of the
medium to oscillate, creating
alternating regions of higher and
lower pressure.

3. Properties of
Sound Waves
It helps to think of sound waves in terms of
what we already know:
Sound is a longitudinal wave
The molecules in the medium (air) oscillate
parallel (or antiparallel) to the direction of
motion of the wave
!
The figure represents the air
molecules being displaced
from one area to another

4. Compression &
Rarefaction
When a sound wave passes through air it causes
regions of higher pressure (compression) and lower
pressure (rarefaction)
!
!
!
!
!
The medium is compressed above the
normal pressure causing an increase
in pressure
The medium is stretched which
causes a lowering of pressure since
the molecules become stretched apart
Note: Pressure variations are scalar and particle displacements are
either parallel or antiparallel
Taken from Physics for Scientists
and Engineers

5. The Speed of
Sound
The speed of a sound wave depends on the properties
of the medium through which it is propagating.
Usually we would calculate speed using :
v = velocity
Ts = Tension in the string/stiffness in the medium
µ = Linear mass density of the string/how much
the spring is oscillating
BUT WAIT

6. The Speed of
Sound
How can we determine how “stiff” the air is?
Instead, we have to use the equation
Where B (bulk modulus) =
The ratio of the change in pressure 𝛥p
divided by the fractional change in the
volume (𝛥V/V)
The negative sign indicates that the sign of 𝛥V/V is
opposite the sign of 𝛥p.

7. Displacement
Amplitude
Just like when we studied SHM we can
also describe sound waves using a
sinusoidal equation
s(x,t) = sm cos(kx- ωt + )
!
http://www.sengpielaudio.com/
WavesSinusodialTimeDistance.gif

8. Displacement
Equation
s(x,t) = sm cos(kx- ωt + )
We use s to denote position
sm is the maximum displacement from equilibrium (the
amplitude for sound waves)
k= (2π/λ). It is representative of the wave number
Remember: v= λ𝒇 = ω/k
ω= 2π𝒇= 2π/T. It is the angular frequency
represents the phase constant

9. Pressure in a
Sound Wave
Not only do we describe position but we
can also relate pressure to a sound wave
The variation in pressure is due to the
increases and decreases in pressure
from the ambient pressure
Ambient pressure: Pressure that
comprises the gas in which a wave
travels through

10. Pressure Equation
The equation for pressure in a sound wave is:
!
In the pressure equation, B (bulk modulus) appears
because it helps us relate volume change and pressure
change.
There is a more specific description of how the
equation is described on pg. 427 of the textbook but
put simply, the equation for pressure is the derivative
(with respect to x) of the displacement equation
multiplied by the bulk modulus.

11. Intensity
The energy of a sound wave is the intensity
(I)
I = wave of power delivered per unit
area
I = P/A
P is the rate at which the wave delivers
energy and A is the area that the wave
is hitting

12. Intensity
The power of a mechanical wave is described as
Pavg= (1/2)µvω
2
A
2
For a sound wave, µ (with units kg/m) is
replaced by ρ — mass density (with units kg/m
3
).
This will give us units W/m
2
. A is replaced by sm
since sm describes the amplitude of a sound wave
The equation becomes: where ω is the
angular frequency, v is the wave speed and ρ is
the density of the medium