Question

Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave: y(x,t) = (63.2 cm) * sin(1.4*x - 2.1 s-1*t + 0.24 rad); with x in meters and t in seconds. What is the phase difference between them? Give answer in radians. Do not enter unit. What is their amplitude? What is the wavelength of the two waves? What is their period?

Answer 1

Given:

A general form of a sinusoidal wave is

where A is the amplitude of the wave, ω is the wave's angular frequency, K is the wavenumber, and ϕ is the phase of the sine wave given in radians. Now similar sine wave but differ by a phase shift can be expressed as:

When these two waves exist in the same medium, the resultant wave resulting from the superposition of the two individual waves is the sum of the two individual waves:

Since

Comparing equation (i) and equation (ii)

Solution for phase angle:

Solution for Amplitude:

(Since cos 0.24= 0.97)

Hence

Solution for wavelenght:

K=1.4

If is wave length then its relation ship with K will be:

(Since x is in meter and radians)

Solution for periods:

Angular frequency

( T is Time period and has a relation with angular frequency)

(since radians)

Sec