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. $y=0.5\sin (\pi x-2\pi t)$
• B. $y=0.5\sin (2\pi x-4\pi t)$
• C. $y=0.5\sin (2\pi x+4\pi t)$
• D. $y=0.5\sin (2\pi x+2\pi t)$

Answer 1

Answer: (C)

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

Equation of a transverse wave propagating in the negative x direction can be written as $y=A\sin (kx+wt)$

Now, amplitude $A=0.5m$

Given : $\lambda =1m$ $\nu =2Hz$

So, $w=2\pi \nu =2\pi \times 2=4\pi$

Also, $k=\frac{2\pi }{\lambda }=\frac{2\pi }{1}=2\pi$

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

Option C is correct.