Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm . The phase difference between the indi

Question

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm . The phase difference between the individual waves is _____ degree.

TestHub · Accepted Answer

If two waves have the same amplitude, frequency, and direction, but are out of phase by $ϕ$ degrees, then the amplitude of the resultant waves is given by $A_{R} = 2 A \cos (\frac{Δ ϕ}{2})$

Here, $A_{1} = A_{2} = A_{R} = 8 cm$

So, $\cos (\frac{Δ ϕ}{2}) = \frac{1}{2}$

Or phase difference between the individual waves is $\frac{Δ ϕ}{2} = 60 ° \Rightarrow Δ ϕ = 120 °$ .

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