Displacement of sound waves

2-3 Traveling sound waves

The longitudinal displacement s(x,t) along the x-axis is plotted along the y-axis.

s(x,t)

s(x,t) denotes the longitudinal displacement of of the particles from their equilibrium positions at x.

When you moves the piston in a sinusoidal manner, the air next to the piston expands and contracts in a sinusoidal manner. Because of the elasticity of air, a longitudinal sinusoidal traveling wave is generated.

Displacement of sound waves

The displacement amplitude s_m is the maximum displacement of the air particles from their equilibrium positions.

Displacement of the air particles form their equilibrium positions

Piston

Air particles

When you push the piston forward, it compresses the air next to it. Consequently, the density and the pressure of the air next to the piston rise above the normal values. Because of the elasticity of air, the region with higher pressure moves forward.

k is the angular wave number.
x is the equilibrium position of the particles.
w is the angular wave number.
t is the time.
f is the phase constant.

When you push the piston backward, it expands the air next to it. Consequently, the density and the pressure of the air next to the piston drop blow the normal values. Because of the elasticity of air, the region with lower pressure moves forward.

Since it is difficult to plot s(x,t) along the x-axis, we will plot the longitudinal displacement along the y-axis. This is just to help us to visualize the displacement and it does not mean that the displacement is along the vertical axis.