Standing Waves 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.

 A physics student plucks a taut 1-meter string fixed at both ends and observes the oscillations. The student measured its mass as 4 g and length as 1 m. The fundamental frequency and amplitude are measured using a high-speed camera coupled to an image processor. The fundamental frequency produced by the oscillating string is 80 Hz, and the amplitude at an antinode is 6 cm. Determine the speed of the waves in the string.

A 0.8 m string with a mass of 1.6 g is attached to a tuning peg on one end and a wooden board on the other. The peg is turned clockwise to obtain an 80-N tension in the string. Calculate the frequency of the fundamental mode of oscillation.

A copper cable is tied between two trees. The horizontal distance between the two trees is 3 m. The transverse waves travel at a speed of 80 m/s along the taut cable. Calculate the i) wavelength and ii) frequency of the third overtone.

A violin's nylon string of length 0.51 m is fixed at both ends. A transverse wave on this string travels at a speed of 600 m/s. Determine i) the wavelength and ii) the frequency of the third harmonic.

The speed of transverse waves in a stretched guitar string is 417 m/s. Determine the first harmonic i) wavelength and ii) frequency if the string length is 75 cm.