Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

Two waves propagating in the same direction through the same region...

Two waves propagating in the same direction through the same region possess equal frequencies, wavelengths, and amplitudes. If each wave has an amplitude of

4 \text{ mm}

and the phase difference between the waves is

90^{}^{{}^{\circ}}

, what is the resultant amplitude?

Options

A $4 \text{ mm}$
B $4\sqrt{2} \text{ mm}$
C $8 \text{ mm}$
D $2\sqrt{2} \text{ mm}$

Correct answer

B. $4\sqrt{2} \text{ mm}$

Step-by-step solution

The resultant amplitude

A_R

of two waves with amplitudes

A_1

and

A_2

and a phase difference

\phi

is given by:

A_R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos\phi}

Given

A_1 = A_2 = 4 \text{ mm}

and

\phi = 90^{}^{{}^{\circ}}

.

Substituting the values:

A_R = \sqrt{4^2 + 4^2 + 2(4)(4) \cos 90^{}^{{}^{\circ}}}

Since

\cos 90^{}^{{}^{\circ}} = 0

A_R = \sqrt{16 + 16 + 0} = \sqrt{32} = 4\sqrt{2} \text{ mm}

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