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PRACTICE / Longitudinal waves

Compression is a spatial change of displacement

A small longitudinal wave has displacement ξ(x,t) = A cos(kx − ωt) along x. Here A = 0.10 mm, k = 5 m⁻¹ and the fluid bulk modulus is 2.0×10⁶ Pa.

What is the amplitude of its pressure perturbation?

Organize the givens & assumptions
  • A = 0.10 mm
  • k = 5 m⁻¹
  • B = 2.0×10⁶ Pa

Linear one-dimensional compression; pressure perturbation δp = −B ∂ξ/∂x. The displacement direction is parallel to propagation, and equilibrium density changes are small.

  1. A200 Pa200\ \mathrm{Pa}
  2. B106 Pa10^6\ \mathrm{Pa}
  3. C0 Pa0\ \mathrm{Pa}
  4. D1000 Pa1000\ \mathrm{Pa}

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