Question

A transverse wave on a taut string is modeled with the wave function y(x, t) = Asin(kx-wt)=(0.2m)sin(6.28m-1 x – 1.57s-1 t) Find the: (a) amplitude, (b) wavelength, (c) period, (d) speed of the wave.

Answer 1

The general equation for the transverse wave is given as follows:

$$y(x,t) = A\sin \left(\dfrac{2\pi}{\lambda}x - 2\pi ft \right)$$

where $A$ is the amplitude, $\lambda$ is the wavelength, $f$ is the frequency of the wave, $v = \lambda f$ is its speed and $T = 1/f$ is its period.

Comparing this expression with the given one, find:

$$A = 0.2m\\ \dfrac{2\pi}{\lambda} = 6.28\Rightarrow\lambda \approx 1m\\ 2\pi f = 1.57\Rightarrow f\approx 0.25Hz\\ T = 1/f \approx 4s\\ v = \lambda f = 0.25m/s$$

Answer. a) 0.2m, b) 1m, c) 4s, d) 0.25 m/s.