Strings satisfy an important equation known as the wave equation. The solution to the wave equation of a point on the string over time can be given as:

, where is the harmonic, is the length of the string.

Determine the period of the fundamental frequency.

Wave 1 has an amplitude of .

Wave 2 has an amplitude of .

What is the maximum and minimum amplitude of these waves when they undergo interference with each other?

What is the fundamental frequency of a standing wave traveling at a speed of through a string of length ?

Given an open pipe of length , what is its fundamental frequency?

Assume the wave passing through the pipe is a sound wave with velocity :

Which of the following is a standing wave?

Given a string of length 2m with two fixed ends, what is the longest wavelength of a standing wave that is possible?

Some students are trying to determine the depth of a well. They drop a stone from rest and time the fall to the well's bottom. They find the time to be with an experimental uncertainty of . Since they need to know the depth with more precision, they create a pure sound tone at the top of the well and note a resonance when the tone has a frequency of . The speed of sound on that day was . How deep was the well?

What is the wavelength produced on the third harmonic of a long open pipe?

Suppose that a pipe open at one end supports a wave whose wavelength is . If this wave is on its third harmonic, how long is the pipe?

A guitar string has a length of . If the string is vibrating with a wavelength of , what harmonic is it vibrating at?