Q. A transverse wave of amplitude $0.5\ m$ and wavelength $1\ m$ and frequency $2\ Hz$ is is propagating in a string in the negative $x$-direction. The expression for this wave is
A) $y(x,t) = 0.5\sin{(2\pi x - 4\pi t)}$
B) $y(x,t) = 0.5\cos{(2\pi x + 4\pi t)}$
C) $y(x,t) = 0.5\sin{(\pi x - 2\pi t)}$
D) $y(x,t) = 0.5\cos{(2\pi x + 2\pi t)}$
Explanation
(b) $\because y = a\cos\left( \frac{2\pi}{\lambda}vt + \frac{2\pi x}{\lambda} \right) = 0.5\cos{(4\pi t + 2\pi x)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.