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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 is340 N. Calculate the mass per unit length of the string

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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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