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 () 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 /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 (linear mass density)
with rho (mass density). This substitution gives a new unit of W/m2
(Power/area = I) Therefore