One pane of a double-glazing unit is thick glass with

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Vibrating bodies, musical and architectural acoustics

Bending, Ringing, Breaking and Flowing, Ch Vibrations of rods, beams and plates

Problem

One pane of a double-glazing unit is

4\,\mathrm{mm}

thick glass with

E = 70\,\mathrm{GPa}

\nu = 0.22

and

\rho = 2500\,\mathrm{kg\,m^{-3}}

. Taking the speed of sound in air as

c = 343\,\mathrm{m\,s^{-1}}

, find the coincidence frequency

f_c = (c^2/2\pi)\sqrt{\rho h/D}

of this pane, where

D = Eh^3/[12(1-\nu^2)]

is the flexural rigidity. State whether this pane's coincidence dip lies at a higher or lower pitch than the

2.0\,\mathrm{kHz}

dip of a

6\,\mathrm{mm}

pane of the same glass.

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