Question

Two waves with an amplitude of 54 units and 64 units arrive at a point in a medium simultaneously. If the two waves are in phase with each other, what is the resultant amplitude of the wave? HELP!!!! :D

Answer 1

The amplitude is 10 hope it helps

Answer 2

The correct answer to the question is 118 units .

CALCULATION:

Let the amplitude of the two waves are denoted as A and B.

The amplitude of the two waves are given as 54 units and 64 units.

Here, A = 54 units

         B = 64 units.

As per the question, the two waves are in phase with each other.

Hence, the phase between these waves $\theta = 0^{0}$.

We are asked to calculate the net amplitude of the resultant wave.

We know that constructive interference will occur when two waves in phase will superimpose each other . Hence, the amplitude of resultant wave will be increased.

Let the amplitude of the resultant wave is R.

The amplitude of the resultant wave when two waves do constructive interference is calculated as -

                                         R = $\sqrt{A^2+B^2+2ABcos\theta}$

                                            = $\sqrt{A^2+B^2+2AB\times cos0}$

                                            = $\sqrt{A^2+B^2+2AB}$  [cos0 = 1]

                                            = $\sqrt{(A+B)^2}$

                                            = $A+B$

                                            = 54 units + 64 units

                                           = 118 units.                               [ans]