Two sound waves having same amplitude ' A ' and angular frequency. ' ω ' but having a phase difference of ( 2 π ) c are superimposed then the maximum amplitude of the resultant w

Question

Two sound waves having same amplitude ' A ' and angular frequency. ' ω ' but having a phase difference of ( 2 π ​ ) c are superimposed then the maximum amplitude of the resultant wave is

TestHub · Accepted Answer

The amplitude of the resultant wave after the superposition of two waves is given by the formula:

$A_{R} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos ϕ$

Given that the amplitudes of both waves are equal, $A_{1} = A_{2} = A$ , and the phase difference is $ϕ = \frac{π}{2}$ .

Substituting these values into the formula:

$A_{R} = A^{2} + A^{2} + 2 (A) (A) cos (\frac{π}{2})$

Since $cos (\frac{π}{2}) = 0$ :

$A_{R} = A^{2} + A^{2} + 0$

$A_{R} = 2 A^{2}$

$A_{R} = 2 A$

The maximum amplitude of the resultant wave is $2 A$ .

Answer: $2 A$

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