Newton’s Laws of Motion

For waves on a string, the restoring

force is provided by the tension T in the string.

The inertial property will in this case be linear

mass density μ, which is mass m of the string

divided by its length L. Using Newton’s Laws of

Motion, an exact formula for the wave speed on

a string can be derived, but this derivation is

outside the scope of this book. We shall,

therefore, use dimensional analysis. We already

know that dimensional analysis alone can never

yield the exact formula. The overall

dimensionless constant is always left

undetermined by dimensional analysis.

The dimension of μ is [ML–1] and that of T is

like force, namely [MLT–2]. We need to combine

these dimensions to get the dimension of speed

v [LT–1]. Simple inspection shows that the

quantity T/μ has the relevant dimension

2

2 2

1

MLT

L T

ML

Thus if T and μ are assumed to be the only

relevant physical quantities,