The speed of a transverse wave on a string is 110 m s−1. The tension in the string is340 N. Calculate the mass per unit length of the string
Question
The speed of a transverse wave on a string is 110 m s−1. The tension in the string is 340 N. Calculate the mass per unit length of the string.
Solution
The speed (v) of a wave on a string is given by the formula:
v = sqrt(T/μ)
where T is the tension in the string and μ is the mass per unit length (linear density) of the string.
We can rearrange this formula to solve for μ:
μ = T/v²
Substituting the given values:
μ = 340 N / (110 m/s)²
μ = 340 N / 12100 (m²/s²)
μ = 0.0281 kg/m
So, the mass per unit length of the string is 0.0281 kg/m.
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