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Q.
A wave is given by the equation
$y=10 \sin 2 \pi(100 t-.02 x)+10 \sin 2 \pi(100 t+.02 x)$.
The loop length of the stationary wave produced will be
Waves
Solution:
The given equation can be represented as
$y=2 \times 10 \cos \left(\frac{2 \pi x}{50}\right) \sin \left(\frac{2 \pi}{50} 5000 t\right)$
Comparing it with standard equation of stationary wave
$\frac{2 \pi}{\lambda}=\frac{2 \pi}{50}$
$\lambda=50$ units
So loop length $\lambda / 2=25$ units.