Standing Waves in Pipes/Strings – AP Physics 1

Boundary Conditions

$$ \lambda = \frac{2L}{n} \quad (n=1,2,3...) $$

The fundamental wavelength $\lambda$ dictated by the physical boundaries. The wave speed $v$ determines the final resonant frequency $f = v/\lambda$.

Key Features

Node: Points of zero displacement (destructive interference).

Antinode: Points of maximum amplitude (constructive interference).

String: Fixed at both ends (Nodes at ends).

Open Pipe: Open at both ends (Antinodes at ends).

Closed Pipe: Closed at one end (Node), open at other (Antinode).

Tags

wavesresonanceharmonicsacoustics

Resonance Properties

Boundary Configuration

Harmonic Number ($n$) 1

Wave Velocity ($v$) 343 m/s

For Strings, Velocity relates to Tension and density ($v = \sqrt{T/\mu}$). For Pipes, it's the speed of sound in air ($v_{sound} \approx 343$ m/s).