Q. Equation of progressive wave is $y = a\sin\left\lbrack 10\pi x + 11\pi t + \frac{\pi}{3} \right\rbrack$
A) Its wavelength is 0.2 units
B) It is travelling in the positive x-direction
C) Wave velocity is 1.5 unit
D) Time period of SHM is 1 s
Explanation
(a) The standard equation is
$y = a\sin{2\pi}\left( \frac{t}{T} - \frac{x}{\lambda} + \phi \right)\ \ \ \ ..(i)$
Dividing multiplying the given equation by 2, we get
$y = a\sin{2\pi\left( \frac{10}{2}x + \frac{11}{2}t + \frac{1}{6} \right)}\ \ \ldots(ii)$
On comparing Egs. (i) and (ii), we get
Λ=0.2 units
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.