Question

Two sinusoidal waves traveling in opposite directions interfere to produce a standing wave with the wave function y = (2.00) sin(0.500x) cos(300t) where x and y are in meters and t is in seconds. (a) Determine the wavelength of the interfering waves. m (b) What is the frequency of the interfering wave? Hz (c) Find the speed of the interfering waves.

Answer 1

Answer:

Part a)

$\lambda = 4\pi$

Part b)

$f = 47.7 Hz$

Part c)

$v = 600 m/s$

Explanation:

Part a)

As we know that angular wave number is given as

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

$k = 0.500$

$0.500 = \frac{2\pi}{\lambda}$

$\lambda = \frac{2\pi}{0.500}$

$\lambda = 4\pi$

Part b)

As we know that angular frequency is given as

$\omega = 300 rad/s$

$\omega = 2\pi f$

$300 = 2\pi f$

$f = \frac{300}{2\pi}$

$f = 47.7 Hz$

Part c)

Speed of the wave is given as

$v = \lambda \times frequency$

so we have

$v = 4\pi \times 47.7$

$v = 600 m/s$