High School

A particular steel guitar string has a mass per unit length of 1.95 g/m.

a) If the tension on this string is 66.9 N, what is the wave speed on the string?

Answer :

The wave speed on a string is given by the equation:

v = sqrt(T/μ)

where v is the wave speed, T is the tension in the string, and μ is the linear mass density of the string (mass per unit length).

In this case, the linear mass density of the steel guitar string is given as 1.95 g/m, which can be converted to SI units as:

μ = 1.95 g/m ÷ 1000 g/kg = 0.00195 kg/m

The tension on the string is given as 66.9 N. Substituting these values into the equation for wave speed, we get:

v = sqrt(T/μ) = sqrt(66.9 N / 0.00195 kg/m) = 121.5 m/s

Therefore, the wave speed on the steel guitar string is 121.5 m/s.

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