Question

A transverse wave of amplitude 0.5 m and wavelength 1 m and frequency 2 Hz 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. $y(x,t) = 0.5\cos(2\pi x + 2\pi t)$

Answer 1

Answer: (B)

$y(x,t) = 0.5\cos(2\pi x + 4\pi t)$

Answer 2

$\because$ $y = a\cos\left( \frac{2\pi}{\lambda}vt + \frac{2\pi x}{\lambda} \right) = 0.5\cos(4\pi t + 2\pi x)$