Question

Suppose you observed the equation for a traveling wave to be y(x, t) = A cos(kx − ????t), where its amplitude of oscillations was 0.15 m, its wavelength was two meters, and the period was 2/15 s. If a point on the wave at a specific time has a displacement of 0.12 m, what is the transverse speed of that point?

Answer 1

Answer:

15m/s

Explanation:

The equation for a traveling wave as expressed as y(x, t) = A cos(kx − $\omega$t) where An is the amplitude f oscillation, $\omega$ is the angular velocity and x is the horizontal displacement and y is the vertical displacement.

From the formula; $k =\frac{2\pi x}{\lambda} \ and \ \omega = 2 \pi f$ where;

$\lambda \ is\ the \ wavelength \ and\ f \ is\ the\ frequency$

Before we can get the transverse speed, we need to get the frequency and the wavelength.

frequency = 1/period

Given period = 2/15 s

Frequency = $\frac{1}{(2/15)}$

frequency = 1 * 15/2

frequency f = 15/2 Hertz

Given wavelength $\lambda$ = 2m

Transverse speed $v = f \lambda$

$v = 15/2 * 2\\\\v = 30/2\\\\v = 15m/s$

Hence, the transverse speed at that point is  15m/s