- Sound waves are longitudinal waves that propagate in three dimensions through pressure variations caused by particle displacements. - The speed of sound can be calculated using the bulk modulus and density of the medium using the equation v=√B/ρ. - The mathematical description of the displacement amplitude of a sound wave is s(x,t)=smcos(kx-ωt+φ), where sm is the maximum displacement, k is the wave number, ω is the angular frequency, and φ is the phase constant. - The relationships between displacement, pressure, and intensity can be determined from the equations Δp(pressurechange)=Bk smsin(kx-ωt+φ) and I=1/2

1. Sound Waves
-Sound waves are longitudinal waves
Sound waves propagate in three dimensions
Pressure variation when particle make displacements.
-The speed of sound
Bulk modulus:
B=-the ratio of change in pressure/the fractional change in the volume
v=√B/ρ
-Mathematical Description of the Displacement Amlitude
s(x,t)=smcos(kx-ωt+φ)
smis the maximum displacement
k is the wave number
k=2π/λ
-Relationships between displacement, pressure and intensity
Δp(pressurechange)=Bk smsin(kx-ωt+φ)
Intensity=Power/Area
I=P/A
I=1/2ρvω^2sm^2

2. 2
0 1 2 3 4 x(m)
Question：Please write the wave function for this wave showed in the picture if the T
for the wave is 1s.
s(x,t)=__________________________________
(Answer in the next page)

3. Answer:
General wave function:
s(x,t)=smcos(kx-ωt+φ)
We can find that the maximum displacement (sm) is 2
K=2π/λ=2π/2
ω=2πf=2π/T=2π/1
φ=-π/2
s(x,t)=2cos(πx-2πt-π/2)