Question

A wave in a string has an amplitude of $2cm$. The wave travels in the +ve direction of x-axis with a speed of $128m{s}^{-1}$ and it is noted that $5$complete waves fit in 4m length of the string. The equation describing the wave is

• A. $y=\left(0.02\right)msin(7.85x+1005t)$
• B. $y=\left(0.02\right)msin(15.7x-20105t)$
• C. $y=\left(0.02\right)msin(15.7x+20105t)$
• D. $y=\left(0.02\right)msin(7.85x-1005t)$

Answer 1

The correct option is D $y=\left(0.02\right)msin(7.85x-1005t)$

Amplitude $=2cm=0.02m$

$v=128m/s$

$5\lambda =4⟹\lambda =\frac{4}{5}=0.8m$

$\nu =\frac{128}{0.8}=160Hz$

$\omega =2\pi \nu =2\pi \times 160=1005$

$k=\frac{2\pi }{\lambda }=\frac{2\pi }{0.8}=7.85$

Therefore,

$y=0.02sin(7.85x-1005t)$