Standing Waves

About this simulation

Standing Waves shows a string fixed at both ends supporting harmonics n = 1 to 8. Students change the harmonic number, wave speed and string length, and can display the two traveling waves whose sum forms the standing wave. Readouts show frequency, wavelength and the count of nodes and antinodes. The animation is slowed so it can be seen, while the frequency readout stays real. It connects wavelength to string length and explains how musical instruments produce notes.

What students can explore

Step Harmonic n from 1 to 8 and watch the number of nodes increase.
Turn Show the two travelling waves on and see how they add.
Double the String length and compare the Frequency readout.
Raise Wave speed and predict the new frequency before reading it.
Count nodes and antinodes and check them against the readout.

Learning objectives

1Explain how a standing wave forms from two traveling waves.
2Identify nodes and antinodes.
3Use f = n v over 2L to find harmonic frequencies.
4Relate string length and wave speed to musical pitch.

Questions teachers ask

Is the Standing Waves simulation free?

Yes. It is free to use, needs no sign-up and runs in any modern browser, including whiteboards, tablets and Chromebooks.

Why are only certain harmonics possible?

Both ends are fixed, so each end must be a node. Only wavelengths that fit a whole number of half-waves into the string length meet that condition.

How do I use it?

Choose a harmonic with the n slider, then change wave speed and string length. Turn on the traveling waves to see the two parts, and read frequency and wavelength from the readouts.

Why does a shorter string sound higher?

The wavelength is 2L over n, so a shorter string has a shorter wavelength. With the same wave speed, the frequency is higher, which we hear as a higher pitch.

Embed this simulation

Drop it into your LMS, blog, or class site — free.

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