Standing Wave Lab

Class XI · Waves: harmonics on a string, v = √(T/μ), λ = 2L/n.

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node antinode

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Harmonic n3

Tension T20.0 N

Linear density μ0.010 kg/m

Length L1.00 m

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v = √(T/μ)44.72 m/s

λ = 2L/n0.667 m

f = v/λ67.08 Hz

T = 1/f14.91 ms

Nodes4

Antinodes3

Formula

Standing wave on a string:
  y(x,t) = A sin(nπx/L) · sin(2π f t)

Speed       v = √(T/μ)
Wavelength  λ = 2L/n          (n = 1,2,…)
Frequency   fₙ = n v / (2L)

Nodes:      x = kL/n,  k = 0..n
Antinodes:  x = (2k+1)L/(2n)

Try this: Quadruple T: v doubles, so every harmonic frequency doubles. Or quadruple μ: v halves. Push n from 1 → 6: count the nodes (n+1) and antinodes (n). That counting trick is gold on JEE waves problems.

Standing Wave Lab

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