A string (L=1m, v=10 m/s) — what are the first three harmonic frequencies?

F_n = nv/(2L) → f₁=5Hz, f₂=10Hz, f₃=15Hz.

How does doubling the string tension change wave speed?

V ∝ √T → speed increases by √2 ≈ 1.41×.

Why do nodes not move in standing waves? What is happening physically?

Incident and reflected waves cancel exactly at nodes through destructive interference.

Pro 🔒~20 min

Wave on a String

Explore transverse waves, reflection, and standing waves

How it works

Transverse waves on a string propagate with speed v = √(T/μ), where T is tension and μ is linear mass density. When the wave reflects from a fixed end, the incident and reflected waves superpose. At specific frequencies, standing waves form with permanent nodes (zero amplitude) and antinodes (maximum amplitude). The allowed frequencies are harmonics: f_n = nv/(2L) for a fixed string of length L.

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Step-by-step

Use the oscillator to shake the string end.
Adjust frequency to find standing waves — the string resonates at harmonics.
Use the ruler to measure wavelength.
Toggle between fixed and free end to see different reflection behavior.
Enable slow motion to see individual wave crests.

Key formulas

$v = \sqrt{\frac{T}{\mu}}$ Wave speed on string (T=tension, μ=linear density)
$v = f\lambda$ Wave speed
$f_n = \frac{n}{2L}v$ Standing wave harmonics

Frequently asked questions

A string (L=1m, v=10 m/s) — what are the first three harmonic frequencies?: F_n = nv/(2L) → f₁=5Hz, f₂=10Hz, f₃=15Hz.
How does doubling the string tension change wave speed?: V ∝ √T → speed increases by √2 ≈ 1.41×.
Why do nodes not move in standing waves? What is happening physically?: Incident and reflected waves cancel exactly at nodes through destructive interference.