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 $128m/s$ and it is noted that 5 complete waves fit in $4m$ length of the string. The equation describing the wave is

• A. y = (0.02) m sin (15.7 x -2010t)
• B. y = (0.02) m sin (15.7 x+ 2010t)
• C. y= (0.02) m sin (7.85 x- 1005t)
• D. y= (0.02) m sin (7.85 x + 1005t)

Answer 1

Answer: (C)

Amplitude $=2cm=0.02m,v=128m/s$
$\lambda ={}_5^4=0.8m;v=\frac{128}{0.8}=160Hz$
$\omega =2\pi v=2\pi \times 160=1005;k=\frac{2\pi }{\lambda }=\frac{2\pi }{0.8}=7.85$
$\therefore y=0.02\sin (7.85x-1005t).$