Waves

Important Formulas

frequency = cycles/second
frequency = 1 / period
Period = T
V = $\frac{\lambda}{T} = f*\lambda$

Mechanical Waves

Example: A lonely fisherman is sitting on a pier and counting incoming water waves. He notes that these waves are sinusoidal and have a crest to crest distance of 5.5 meters. If a wave hits the pier every 2.1 seconds, what is the frequency and speed of the wave?

Given info: $\quad T=2.1seconds\quad \lambda=5.5 meters$

frequency = $\frac{1}{T} = \frac{1}{2.1 seconds} = 0.476 Hz$

velocity = $\frac{\lambda}{T} = f*\lambda = (0.476)*(5.5 m) = 2.619 m/s$

so… $\quad f= 0.476 Hz \quad and \quad v = 2.619 m/s$

Air Waves

Waves in air have similar calculations, however it is important to know that the velocity is determined by atmospheric conditions. At standard temperature and pressure (STP), mechanical waves are fixed at 343 m/s for their velocity. Due to the constant velocity, the wavelength and frequency become inversely proportional, $(V = \lambda*f)$ . Doppler effect/Doppler shift. Light also has similar velocity limitations. The speed of light is fixed at approximately 3×108 m/s. Light waves are not mechanical waves and therefore they do not need a medium (such as air or water) to travel.