Wave motionMediumBloom L3

Question

A wave is represented by the equation y = 10 sin 2π(100t−0.02x) + 10 sin 2π(100t+0.02x). The maximum amplitude and loop length are respectively

Options

A.20 units and 30 units
B.20 units and 25 units
C.30 units and 20 units
D.25 units and 20 units

Solution

Sol. y = 10 sin2π(100τ – 0.02x) + 10 sec2π(100t + 0.02x)

y = 20 sec[200πt] cos2π[0.02x]

= $\frac{20\cos 2\pi(0.02x)}{A}\sin 200\pi t$

Amax = 20

Loop length = $\frac{\lambda}{2}$

$\lambda = \frac{2\pi}{k} = 50m$

Loop length = 25m

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