Question

Transverse waves on a string have wave speed $12.0$ m/s, amplitude $0.05m$ and wavelength $0.4m$. The waves travel in the $+x$ direction and at $t=0$, the $x=0$ end of the string has zero displacement and is moving upwards. Find the transverse displacement of a point at x = 0.25 m at time t = 0.15 s.

• A. $-4.54cm$
• B. $-5.54cm$
• C. $-3.54cm$
• D. $-9.54cm$

Answer 1

The correct option is C $-3.54cm$

A wave traveling in +x direction is represented by $y=Asin(\omega t-kx)$

where $\omega =2\pi \nu$

and $k=\frac{2\pi }{\lambda }$

We know that speed of wave=$v=\lambda \nu$

Thus here

$\omega =2\pi \times \frac{v}{\lambda }=2\pi \times \frac{12}{0.4}=60\pi s^{-1}$

and $k=\frac{2\pi }{0.4}=5\pi m^{-1}$

Thus wave is $y=\left(0.05m\right)sin\left(\right(60\pi s^{-1})t-(5\pi m^{-1}\left)x\right)$

Thus the displacement of point at $x=0.25m$ and $t=0.15s$ can be found by putting the values in the equation of wave.

Thus $y(x=0.25m,t=0.15s)=-0.0354m=-3.54cm$