University of British Columbia Physics 101 L2H Learning Object Assignment 1

1. Sound Waves
Learning Object (LO4)
Naysilla Dayanara
Section L2H

2. Longitudinal Waves
❖ Waves in which the displacement of the medium is in the same direction, or opposite to,
the direction of travel.

3. Medium
The molecules of the medium
oscillate as sound wave
passes through
“Stretched” = Rarefraction
PRESSURE IS LOWERED
“Compressed”=Compression
PRESSUREISELEVATED

4. Different Ways to Describe Sound
Wave
P vs. position (x)
Displacement (y) vs.
Position (x)

5. How much mass is
oscillating
“Stiffness” in 2D…
How much the length of
the string changes when
we exert a force on it
Speed of Sound
Recall textbook Sec 14-4 (p. 388) on “Wave speed on a String”
Depends on INERTIAL & ELASTIC properties of the medium
Linear mass density
(µ)
Tension of String
which gives us the equation:
“Stiffness” in 3D waves…
Measure by what fraction
the volume changes when
we change the pressure
exerted on the material

6. Speed of Sound
The 3D equivalent of “Stiffness” is called the “Bulk Modulus”
Ratio of (∆P) and fractional change in volume (∆V/V)
Negative (-) sign: because ∆V/V is always opposite of the sign of ∆P
Similar to this equation…
How much mass is
oscillating
Density of medium, how
individual particle oscillates.

7. Displacement, Pressure,
Intensity
At High pressure:
Particles are pushed into it from
left and right.
Hence, at Pmax,
displacement must be 0
Left Side
(+) displacement
Right Side
(-) displacement
Positive Negative
Similarly, at Pmin,
displacement is also 0

8. Amplitude of pressure variation
❖ Comparing equations for ∆P
and s(x,t), we see that
although the wave function
has a cosine function and the
pressure is a sine function,
the arguments are the same
in both cases. They have the
same wavelength, period, and
wave speed but are π/2 out of
phase (between sin and cos)
❖ This relationship is plotted in
the next slide.

9. Comparison

10. Displacement, Pressure,
Intensity
We now examine the energy that a sound wave delivers (INTENSITY):
“Power delivered per unit area”
Where P is the rate at which the wave delivers energy, and A is the area
that the wave is impinging upon.
As shown previously (one dimension)
For a sound wave, replace the µ (linear mass density) with ‘rho’ (mass
density). This substitution gives a new unit of W/m2 (Power/area = I)
Therefore