Waves on a string animation

Animation by Phet

In this simulation you can investigate the behaviour of waves on a string. Download PDF activity sheet

Part 1 Waves on a string with no end

Select the ‘No end’ option and ‘oscillate’.

Challenge: Determine the speed of the waves at each tension setting (high, medium and low).  Explain what measurements you made to calculate the speed.

Settings:          amplitude: 0.75 cm     damping: zero

high tension:

medium tension:

low tension:

Does the speed of the wave depend on the frequency or is it the same for all frequencies? Collect data to support your answer:

Part 2 Waves on a string with a fixed end

The reflected wave interferes with the original wave and creates a standing wave composed of nodes and antinodes if the frequency is just right.  A node will always exist at the fixed end because the phase of the wave is inverted upon reflection and therefore always destructively interferes at that position.  Adjust the frequency until maximum amplitude results.  (You can use the reference line to help you detect small changes in the amplitude as you fine tune the frequency.)

Settings:  amplitude: 0.05 cm                 tension: high                damping: none

Select the ‘fixed end’ option and ‘oscillate’.

Challenge: Find, record frequencies and draw the waveforms for the 4^th, 3^rd, 2^nd, and 1^st harmonics.

 (4 antinodes)           (3 antinodes)               (2 antinodes)           (1 antinode)

f₄ = ________ Hz        f₃ = ________ Hz        f₂ = ________ Hz        f₁ = ________ Hz

Divide each higher harmonic by the first harmonic:

f₄ / f₁ = _____             f₃ / f₁ = _____             f₂ / f₁ = _____

Are the higher harmonics whole-number multiples of the first harmonic (fundamental frequency)? ______

Predict the frequency of the 5^th harmonic: (show calculation)

________________________________________________________________

Set the wave driver to that frequency and draw the result here:

________________________________________________________________

Part 3 Waves on a string with a loose end

The reflected wave interferes with the original wave and creates a standing wave composed of nodes and antinodes if the frequency is just right. Instead of a node, an antinode will always exist at the loose end. (This happens because the phase of the wave is not inverted upon reflection from a loose end and therefore always constructively interferes at that position.)

Challenge: Draw and measure the frequency of the 1^st harmonic (node near driver end followed by an antinode on loose end)

Settings:   amplitude: 0.05 cm                 tension: high                damping: none

Select the ‘loose end’ option and ‘oscillate’

What fraction of a wavelength is this?  __________

f₁ = ________ Hz       

Predict the frequencies of several higher harmonics:

Use the wave simulator to test each of your calculated harmonics.  Note which ones appeared and which ones did not appear!

Draw and label the standing waves for each of the harmonics you discovered:

Divide each higher harmonic by the first harmonic:

Are the higher harmonics even-number or odd-number multiples of the first harmonic? ______

Explain why there are missing harmonics for standing waves on a string with a loose (free) end. (Hint: Is there a pattern to how much of a wavelength fits between the ends of the string with a loose end?)

Next step: The speed of a transverse wave on a string of length L and mass m under tension T is given by the formula

If the maximum tension in the simulation is 10.0 N, what is the linear mass density (m/L) of the string?

Well done for completing the Standing Waves Lab activity.

Click here for an excellent animation to explain standing wave formation by Walter Fendt