Waves, Sound, and Physical Optics

A wave has a frequency of 4 Hz. What is its period?

Given the sinusoidal wave equation $x(t) = 5 \cos(4\pi t)$, what is the amplitude of the wave?

Two waves are described by the equations $y_1(x,t) = 4 \cos(2x - 3t)$ and $y_2(x,t) = -4 \cos(2x - 3t)$. What is the resultant displacement at any point and time?

What is the relationship between the period ($T$) and frequency ($f$) of a wave?

A pendulum completes one full swing in 2 seconds. What is the frequency of this oscillation?

A wave is described by the equation $x(t) = 3\cos(6\pi t)$. What is the displacement of the wave at $t = \frac{1}{6}$ seconds?

A wave completes 5 cycles in 10 milliseconds. What is its frequency?

A simple pendulum in a grandfather clock completes one full swing every 4 seconds. If the pendulum's length is adjusted so that it now completes a swing in 3.5 seconds, what is the new frequency of the pendulum?

For a wave described by the equation $y(x) = 10 \cos(2\pi \frac{x}{5})$, what is the wavelength?

A wave has a speed of 50 m/s and a frequency of 10 Hz. What is its wavelength?