Question

What phase difference between two otherwise identical harmonic waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 0.6 times that of the amplitude of either of the combining waves? Express your answer in degrees.

Answer 1

`\theta=145`

Step-by-step explanation:

The amplitude of he combined wave is:

`B=2Acos(\theta/2)\\`

A, is the amplitude from the identical harmonic waves

B, is the amplitude of the resultant wave

θ, is the phase, between the waves

The amplitude of the combined wave must be 0.6A:

`0.6A=2Acos(\theta/2)\\ cos(\theta/2)=0.3\\\theta/2=72.5\\\theta=145`