Q. A wave in a string has an amplitude of $2\ cm.$ The wave travels in the $+ ve$ direction of $x$ axis with a speed of $128\ m/sec$ and it is noted that 5 complete waves fit in $4\ m$ length of the string. The equation describing the wave is
A) $y = (0.02)m\sin{(7.85\ x + 1005t)}$
B) $y = (0.02)m\sin{(15.7\ x - 2010t)}$
C) $y = (0.02)m\sin{(15.7\ x + 2010t)}$
D) $y = (0.02)m\sin{(7.85\ x - 1005t)}$
Explanation
(d) According to given information $5\lambda = 4 \Rightarrow \lambda = 0.8m$
So, frequency $v = \frac{v}{\lambda} = \frac{128}{0.8} = 160Hz$
and Angular frequency
$\omega = 2\pi v = 2 \times 3.14 \times 160 = 1005\ rad/s$
Also propagation constant $k = \frac{2\pi}{\lambda} = \frac{2\pi}{0.8} = 7.85\ m^{- 1}$
On Putting these values in standard equation option (d) is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.