Question

The wave described by y = 0.35 sin $(2 \pi t - 10 \pi x)$, where x and y are in metres and t in seconds, is a wave travelling along the

• A. negative x-direction with amplitude 0.35 m and wavelength $\lambda = 0.5$ m
• B. wavelength $\lambda = 0.2$ m

Answer 1

The wave travels in the positive $x$-direction with amplitude 0.35 m and wavelength $\lambda = 0.2$ m.

Answer 2

The given wave is

$$y = 0.35 \sin(2\pi t - 10\pi x)$$

A wave in the form

$$y = A \sin(\omega t - kx)$$

travels in the positive $x$-direction.

Here,

$$\omega = 2\pi \quad \text{and} \quad k = 10\pi.$$

The wavelength $\lambda$ is given by:

$$\lambda = \frac{2\pi}{k} = \frac{2\pi}{10\pi} = 0.2 \text{ m.}$$

Thus, the wave has an amplitude of $0.35$ m, wavelength $0.2$ m, and travels along the positive $x$-direction.