Physics

Problem

The displacement

y

of a point on a stretched string carrying a progressive mechanical wave is expressed as

y = a \sin \left(\frac{2\pi x}{\lambda} - \omega t\right),

where

a

and

x

are lengths,

t

is time, and

\lambda

is the wavelength. (i) State the principle that allows you to test whether this equation is dimensionally consistent. (ii) Using that principle, show that the argument of the sine function must be dimensionless and hence obtain the dimensions of the angular frequency

\omega

. (iii) Comment on the dimensions of the numerical factor

2\pi

appearing in the wave equation.

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