Question

1. A wave is described by the wave equation: y(x,t)= 18.2cos(8.2x±10.8t) Determine the frequency of the wave. 
2. Radio waves travel at the speed of light- 300,000 km/s. What is the wavelength of radio waves received at 111.7 MHz on your FM radio dial? 
3.  A wave is described by the wave equation: y(x,t)= 35.5cos(1.2x±4.5t) Determine the amplitude of the wave.

Answer 1

1) We can find the frequency as follows:

$$f=\dfrac{\omega}{2\pi}=\dfrac{10.8\ \dfrac{rad}{s}}{2\pi}=1.72\ Hz.$$

2)

$$\lambda=\dfrac{c}{f}=\dfrac{3\times10^8\ \dfrac{m}{s}}{111.7\times10^6\ Hz}=2.68\ m.$$

3) The amplitude of the wave is 35.5 m.