A string has a tension of 100.0 N and a wave speed of40.0 m/s when it is plucked. What is the linear densityof the string?
Question
A string has a tension of 100.0 N and a wave speed of 40.0 m/s when it is plucked. What is the linear density of the string?
Solution
The wave speed v on a stretched string depends on the tension F and the linear mass density μ (mass/length) of the string. This relationship is given by the formula:
v = sqrt(F/μ)
We can rearrange this formula to solve for the linear density μ:
μ = F/v²
Given that the tension F is 100.0 N and the wave speed v is 40.0 m/s, we can substitute these values into the formula:
μ = 100.0 N / (40.0 m/s)²
μ = 100.0 N / 1600 m²/s²
μ = 0.0625 kg/m
So, the linear density of the string is 0.0625 kg/m.
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