Oscillations and waves

Conditions for a standing wave

Test the condition L = nλ/2 and see how the number of nodes and antinodes changes with frequency or string length. Measure string length and wavelength at resonance, then verify $L = nλ/2$ .

High school

⚠ This is a virtual simulation; do not tension a real string or increase its tension during an experiment.

Equipment

String fixed at both ends with wave speed v = 40 m/s
Frequency f and length L sliders; nearest-resonance control

Procedure

Find the string's resonant modes
Change frequency f or length L with the sliders. Observe when a clear standing-wave pattern appears and read the integer n in the panel: at resonance n = 2Lf/v; both ends are nodes, there are n + 1 nodes including the ends and n antinodes. Press Set nearest resonant frequency to move to the nearest mode, then change L to see which modes still satisfy the condition. Compare the displayed values with $L = nλ/2$ .
Select the nearest resonant mode
Choose a non-resonant frequency and press the nearest-frequency control; observe the string settle into a clear mode. Count the antinodes n and compare with fₙ = nv/(2L), using v = 40 m/s and the displayed length. Compare the displayed values with $f_n = nv/(2L)$ .
Test the effect of string length
Hold f fixed and vary L; observe the antinode and node counts as resonance disappears or returns. Use L = nλ/2 with v = fλ to calculate the wavelength for each mode, then check that both ends remain nodes. Compare the displayed values with $L = nλ/2$ .

Simulation

Experiment history

Standing waves arise when two waves of the same frequency traveling in opposite directions overlap, as with an incoming wave and its reflection on a string. The pattern became an important tool in acoustics and the study of oscillations: nodes remain nearly still while antinodes oscillate with large amplitude. For a string fixed at both ends, each endpoint must be a node, so only certain wavelengths fit the string's length. The resonance condition is L = nλ/2, where n counts antinodes and λ is wavelength; with v = fλ, the allowed frequencies are fₙ = nv/(2L). Raising frequency or shortening the string changes the mode through integer steps rather than producing every stable shape continuously. This simulation holds the wave speed fixed to isolate the roles of f and L. In a real string, tension, mass per unit length, and boundary conditions also determine v, so the observed pattern depends on how the string is driven and supported.

Related physicists

Isaac Newton

Equipment

Procedure

Simulation

Experiment history

Related physicists

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