A set of lecture notes gives the speed of sound in a gas of pressure (unit: pascal, )…

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Quantities, units and the practice of measurement · Quantities, units and the practice of measurement

Measurement and Method, Ch What dimensions decide before you measure anything

Problem

A set of lecture notes gives the speed

v

of sound in a gas of pressure

p

(unit: pascal,

\mathrm{N\,m^{-2}}

) and density

\rho

(unit:

\mathrm{kg\,m^{-3}}

), with

\gamma

a pure number, as

v = \sqrt{\dfrac{\gamma p}{\rho}} + p\rho.

Find the error: identify which term is dimensionally wrong, state its dimension, and explain why no numerical prefactor could ever fix it.

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