A transverse wave travels along a taut string

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Oscillations, Waves & Acoustics · Quantities, units and the practice of measurement

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

Problem

A transverse wave travels along a taut string. The relevant quantities are judged to be the tension in the string,

F

(unit

\mathrm{N}

), and the mass per unit length of the string,

\mu

(unit

\mathrm{kg\,m^{-1}}

). ((a)) Write

v = C F^{\alpha}\mu^{\beta}

for the wave speed

v

, with

C

a dimensionless constant, and use dimensional homogeneity to find

\alpha

and

\beta

. ((b)) For a string with

F = 40\ \mathrm{N}

and

\mu = 1.0\times10^{-3}\ \mathrm{kg\,m^{-1}}

, evaluate

v

in terms of

C

. ((c)) The full wave equation (not derivable from dimensions alone) gives

C = 1

for this problem. State the numerical wave speed to two significant figures.

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