# Prove that sound waves propagate with a speed given by Equation 17.1. Proceed as follows. In Figure

## Question:

Show that ∑Fx = max implies that ─ [∂(ΔP)/∂x] A Δx = pA Δx (∂2s/∂t2). By substituting ΔP = ─ b (∂s/∂t2). To a mathematical physicist, this equation demonstrates the existence of sound waves and determines their speed. As a physics student, you must take another step or two. Substitute into the wave equation the trial solution s(x, t) = smax cos (kx─wt). Show that this function satisfies the wave equation provided that w/t = √B/p. this result reveals that sound waves exist provided that they move with the speed v = fA = (2πf) (A /2π) = w/k = √B/p.

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**Related Book For**

## Fundamentals of Thermodynamics

**ISBN:** 978-0471152323

6th edition

**Authors:** Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen