A violin string has a wave speed of 62 m/s when it isplayed. If the string is 0.60 m long and has a tensionof 200.0 N, what is the mass of the string?
Question
A violin string has a wave speed of 62 m/s when it isplayed. If the string is 0.60 m long and has a tensionof 200.0 N, what is the mass of the string?
Solution
To find the mass of the string, we first need to find the linear density (mass per unit length) of the string. The wave speed v on a string under tension T with a linear density μ is given by the formula:
v = sqrt(T/μ)
We can rearrange this formula to solve for μ:
μ = T/v²
Substituting the given values:
μ = 200.0 N / (62 m/s)² = 0.052 kg/m
Now, to find the mass of the string, we multiply the linear density by the length of the string:
mass = μ * length = 0.052 kg/m * 0.60 m = 0.0312 kg
So, the mass of the string is 0.0312 kg.
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