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 0.65 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.

(a) Number ________________ Units: _____

(b) Number ________________ Units: _____

(c) Number ________________ Units: _____

Answer 1

Solution-

The equations of the two travelling waves be;
Asinωt and Asin(ωt+φ)
here φ = the phase difference
The resultant wave is given by
Y = Asinωt + Asin(ωt+φ)
Y = A 2sin(ωt + φ/2)cos(φ/2)
Y = A'sin(ωt + φ/2)
Where A' = 2Acos(φ/2) is the amplitude of the resultamt wave
Given A' = 0.65A
2Acos(φ/2) = 0.65A
φ = 142.07o
φ = 2.48 rad
Interms of wavelength λ,
φ = 142.07/360 λ
φ = 0.39 λ