A wave is given by the equation y=10 sin 2 π(100 t-.02 x)+10 sin 2 π(100 t+.02 x). The loop length of the stationary wave produced will be

Question

A wave is given by the equation y=10 sin 2 π(100 t-.02 x)+10 sin 2 π(100 t+.02 x). The loop length of the stationary wave produced will be (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The given equation can be represented as

y = 2 \times 10 cos (\frac{2 π x}{50}) sin (\frac{2 π}{50} 5000 t)

Comparing it with standard equation of stationary wave

\frac{2 π}{λ} = \frac{2 π}{50}

λ = 50

units
So loop length

λ /2 = 25

units.

Q. A wave is given by the equation y=10sin2π(100t−.02x)+10sin2π(100t+.02x). The loop length of the stationary wave produced will be

The given equation can be represented as y=2×10cos(502πx​)sin(502π​5000t) Comparing it with standard equation of stationary wave λ2π​=502π​ λ=50 units So loop length λ/2=25 units.

Q. A wave is given by the equation $y = 10 sin 2 π (100 t - .02 x) + 10 sin 2 π (100 t + .02 x)$ . The loop length of the stationary wave produced will be

The given equation can be represented as
$y = 2 \times 10 cos (\frac{2 π x}{50}) sin (\frac{2 π}{50} 5000 t)$
Comparing it with standard equation of stationary wave
$\frac{2 π}{λ} = \frac{2 π}{50}$
$λ = 50$ units
So loop length $λ /2 = 25$ units.