Standing Wave Functions Practice Problems

A string, fixed at its ends, oscillates according to the equation y(x,t) = (3 cm) sin [(π rad/cm) x]sin[(200π rad/s)t]. What is the speed of the two traveling waves that form this standing wave pattern?

A wave traveling along a string is totally reflected on a rigid boundary. The incident and reflected waves produce a standing wave pattern described by y(x,t) = (5 cm) sin [(π/4 rad/cm) x]sin[(30π rad/s)t]. Find the frequency of the incident and reflected traveling waves that make up this standing wave.

Two sinusoidal waves traveling in opposite directions along a string interfere and produce a standing wave pattern. The pattern is described by the equation y(x,t) = 3 sin(π x)sin(50π t) where x and y are in cm and t is in seconds. What is the wavelength of each of the two traveling waves?

A nylon guitar string vibrates according to the equation y = 0.2 sin(2.28 x)sin(40π t) where x and y are in cm and t in seconds. What is the amplitude A of the two transversal waves that form this standing wave pattern?

A second harmonic is generated in an elastic cord of length l stretched between two clamps. The vertical displacement (y) of a cord element as a function of the horizontal position x and time t is given by the equation  . Make a sketch of the standing-wave pattern.