A simple wave motion is represented by y = 5 sin ⁡ 4 π t + 3 cos ⁡ 4 π t . Its amplitude is

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A simple wave motion is represented by

y = 5 (\sin 4 π t + \sqrt{3} \cos 4 π t)

. Its amplitude is

PhysicsOscillationsMHT CETMHT CET 2017

Options:

A $5$ units
B $5 \sqrt{3}$ units
C $10 \sqrt{3}$ units
D $10$ units

Solution:

1498 Upvotes Verified Answer

The correct answer is:

10

units

y = 5 (\sin 4 π t + \sqrt{3} \cos 4 π t)

y = (5 \sin 4 π t + 5 \sqrt{3} \cos 4 π t)

A = \sqrt{A_{1}^{2} + A_{2}^{2}}

A = \sqrt{{(5)}^{2} + {(5 \sqrt{3})}^{2}}

= \sqrt{25 + 75} = \sqrt{100}

A = 10

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