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FLD-17

Speed of sound

c = √(K/ρ). Newton–Laplace speed in a compressible fluid.

Reading speed
FluidsNewton–Laplace

Governing equation

c=K/ρc=\sqrt{K/\rho}

K∈[1×10−4,200]K \in \left[1\times 10^{-4}, 200\right]

where

K
Bulk modulus (GPa)
\rho
Density (kg/m³)
c
Sound speed (m/s)

The figure, part by part

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FLD-17 · wave
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①

Governing law — red

c=K/ρc=\sqrt{K/\rho}

K∈[1×10−4,200]K \in \left[1\times 10^{-4}, 200\right]

K=1×10−4K = 1\times 10^{-4}c=10c = 10

②

Domain of the variable — blue

Kmin⁡=1×10−4,Kmax⁡=200K_{\min} = 1\times 10^{-4},\quad K_{\max} = 200

K∈[1×10−4,200]K \in \left[1\times 10^{-4}, 200\right]

K=1×10−4K = 1\times 10^{-4}K=1×10−4K = 1\times 10^{-4}

③

Response curve — green

c=K/ρc=\sqrt{K/\rho}

K∈[1×10−4,200]K \in \left[1\times 10^{-4}, 200\right]

K=1×10−4K = 1\times 10^{-4}c=10c = 10

④

Rate of change — amber

dcdK\frac{\mathrm{d}c}{\mathrm{d}K}

K∈[1×10−4,200]K \in \left[1\times 10^{-4}, 200\right]

K=1.258K = 1.258c′=626.5c^{\prime} = 626.5

Lecture brief

Historical brief

Bernoulli, Navier–Stokes, Reynolds (1883) and Stokes drag made continuum flow a dimensionless craft. The sheets compute head, drag, Re and a pedagogical NS snapshot. This sheet (FLD-17 — Speed of sound) is the form associated with Newton–Laplace. Working symbols: KK, ρ\rho →\rightarrow cc. Use the adiabatic bulk modulus. In air c = √(γ R T) ≈ 343 m/s at 20 °C.

Purpose

Purpose: compute cc from KK, ρ\rho in Fluid physics via c=K/ρc=\sqrt{K/\rho} c = √(K/ρ). Newton–Laplace speed in a compressible fluid. Use it when a real fluid physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given K=2.200 GPaK = 2.200\,\mathrm{GPa}, ρ=1000.000 kg/m3\rho = 1000.000\,\mathrm{kg/m^{3}}, the governing relation c=K/ρc=\sqrt{K/\rho} yields c=1483.2 m/sc = 1483.2\,\mathrm{m/s}. A pulse, a fluid column, a travel time. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Sound speed c1483.2 m/s
Reading speed

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FLD-17 · wave
00:0 / 00:08

Narration of this film

A pulse, a fluid column, a travel time.

Use the adiabatic bulk modulus. In air c = √(γ R T) ≈ 343 m/s at 20 °C.

Reading speed

Watch on YouTube