A sound wave of frequency 166 Hz travels with a speed 332 ms−1 along positive x-axis in air. Each point of the medium moves up and down through...

The equation of the traveling wave has the following form:

y = A sin(wt ± Kx)

Where:

A, is the amplitude of the wave.

w = 2πf, is the angular frequency.

K = 2π/λ, is the constant of propagation of wave.

The sign is chosen according to the direction of propagation; positive for the negative direction and negative for the positive direction. In our case the direction is positive in x, then the equation is:

y = A sin(wt - Kx)

For the angular frequency, we have:

w = 2πf = 2π*166 = 332π

To find the propagation constant we use the relationship between the speed v and the wavelength λ:

v = λ/T

λ = v*T = v(2π/w) = 332(2π/332π) = 2 m

K = 2π/λ = 2π/2 = π m^-1

So, the wave equation is:

y = 5*10^-3 sin(332πt - πx) m

Two points located at a distance of a wavelength have a phase difference equal to 2π. For two points with a difference of phase 45° = π/4, we have:

x = λ/8 = 2/8 = 0.25 m