Question

The equation of a simple harmonic wave is given by $y=5\, \sin \frac{\pi}{2}(100\, t-x)$, where $x$ and $y$ are in meter and time is in second. The period of the wave in second will be

• A. 0.04
• B. 0.01
• C. 1
• D. 5

Answer 1

Answer: (A)

0.04

Answer 2

The given equation is
$y=5 \sin \frac{\pi}{2}(100 t-x)$ ...(i)
Comparing E (i) with standard wave equation, given by
$y=A \sin (\omega t-k x)$ ...)ii)
we have
$\omega =\frac{100 \pi}{2}=50\, \pi$
$\frac{2 \pi}{T} =50\, \pi$
$\Rightarrow \frac{2 \pi}{T}=50\, \pi$
$\Rightarrow T=\frac{2 \pi}{50 \pi}=0.04\, s$