Q. A plane wave is represented by $x = 1.2\sin{(314t + 12.56y)}.$ Where $x$ and $y$ are distances measured along in $x$ and $y$ direction in meters and $t$ is time in seconds. This wave has
A) A wavelength of $0.25\ m$ and travels in $+ \ ve\ x$ direction
B) A wavelength of $0.25\ m$ and travels in $+ \ ve\ y$ direction
C) A wavelength of $0.5\ m$ and travels in $- \ ve\ y$ direction
D) A wavelength of $0.5\ m$ and travels in $- \ ve\ x$ direction
Explanation
(c) The given equation representing a wave travelling along $- y$ direction (because $' + '$ sign is given between $t$ term and $x$ term).
On comparing it with $x = A\sin{(\omega t + ky)}$
We get $k = \frac{2\pi}{\lambda} = 12.56 \Rightarrow \lambda = \frac{2 \times 3.14}{12.56} = 0.5\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.