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Deduce an expression for the speed of longitudinal wave in a gas.

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The speed of a longitudinal wave is defined in the same was as the speed of transverse waves: Wave speed Wave speed is the distance a wave travels per unit time. Quantity: Wave speed (v) Unit name: speed Unit: m⋅s−1 The distance between two successive compressions is 1 wavelength,...
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The speed of a longitudinal wave is defined in the same was as the speed of transverse waves:

Wave speed

Wave speed is the distance a wave travels per unit time.

Quantity: Wave speed (v)         Unit name: speed         Unit: m⋅s1

The distance between two successive compressions is 1 wavelength, λλ. Thus in a time of 1 period, the wave will travel 1 wavelength in distance. Thus the speed of the wave, vv, is:

v=distance travelledtime taken=λTv=distance travelledtime taken=λT

However, f=1Tf=1T. Therefore, we can also write:

v=λT=λ1T=λfv=λT=λ⋅1T=λ⋅f

We call this equation the wave equation. To summarise, we have that v=λfv=λ⋅f where

  • v=v= speed in m⋅s1m·s−1

  • λ=λ= wavelength in mm

  • f=f= frequency in Hz

 

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