Question

A piano wire has a linear mass density of μ = 4.85 ✕ 10−3 kg/m. Under what tension (in N) must the string be kept to produce waves with a wave speed of 595.00 m/s?

Answer 1

Answer:

The string must have a tension of 1717.021 newtons to have a wave speed of 595 meters per second.

Explanation:

This is a case where transversal waves occur. The formula of speed for transversal waves is:

$v = \sqrt{\frac{T}{\mu} }$

Where:

$v$ - Speed of the transversal wave, measured in meters per second.

$\mu$ - Linear mass density, measured in kilograms per meter.

$T$ - Tension, measured in newtons.

The tension is now cleared:

$T = v^{2}\cdot \mu$

If $v = 595\,\frac{m}{s}$ and $\mu = 4.85\times 10^{-3}\,\frac{kg}{m}$, the tension needed is:

$T = \left(595\,\frac{m}{s} \right)^{2}\cdot \left(4.85\times 10^{-3}\,\frac{kg}{m} \right)$

$T = 1717.021\,N$

The string must have a tension of 1717.021 newtons to have a wave speed of 595 meters per second.