Question

What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 0.64 times that of the common amplitude of the two combining waves? Express your answer in (a) degrees, (b) radians, and (c) as a fraction of the wavelength.

Answer 1

Ф = 142.674 degree

Ф = 2.490131057 rad

wavelength = 0.396316 λ

Step-by-step explanation:

Given data

combined wave having an amplitude 0.64 times

to find out

answer in degrees, radians, and fraction of the wavelength

solution

let us consider these two wave equation

Asin(ωt) and the Asin (ωt + Ф)

and here Ф is phase difference

so we say

resultant wave is

Y = Asin(ωt) + Asin (ωt + Ф) = Asin(ωt + Ф/2) cos ( Ф/2)

so Y = A' sin(ωt + Ф/2)

we know that here resultant wave amplitude is 2A cos ( Ф/2)

so

put A= 0.64 A

so 2Acos ( Ф/2) = 0.64 A

and Ф/2 = 71.3370

Ф = 142.674 degree

Ф = 2.490131057 rad

so wavelength is 2.490131057 / 2π

wavelength = 0.396316 λ