Question

The displacement $y$ (in $cm$ ) produced by a simple harmonic wave is given by : $y=\frac{10}{\pi} \sin \left[2000 \, \pi t-\frac{\pi x}{17}\right] .$ The time period and maximum velocity of the particles in the medium will respectively be :

• A. $10^{-3} s , 330 \,ms ^{-1}$
• B. $10^{-4} s , 20 \,ms ^{-1}$
• C. $10^{-3} s , 200 \,ms ^{-1}$
• D. $10^{-2} s , 2000 \, ms ^{-1}$

Answer 1

Answer: (C)

Comparing given equation with $y=A \sin (\omega t-k x)$ we get
$A=\frac{10}{\pi} cm$
$\omega=2000 \,\pi s ^{-1}$
$T=\frac{2 \pi}{\omega}=10^{-3} s$
Maximum velocity $=\omega A=\frac{10}{\pi \cdot 100} \times 2000 \,\pi=200 \, ms ^{-1}$