Question

A steel of wire has a length of 12m and a mass of 2.10 kg what will be the speed of transverse wave on this wire when a tension of 2.06×10^4N is applied

Answer 1

Answer:

$\boxed{\sf Speed \ of \ transverse \ wave \ (v) \approx 343 \ m/s}$

Given:

Length of the wire (l) = 12 m

Mass of the wire (m) = 2.10 kg

Tension (T) = $\sf 2.06 \times 10^{4}$ N

To Find:

Speed of transverse wave on the given wire

Explanation:

$\sf Mass \ per \ unit \ length \ ( \mu) = \frac{m}{l}$

$\sf \mu = \frac{2.10}{12}$

$\sf \mu = 0.175 \: kg /m$

$\sf \implies Speed \ of \ transverse \ wave \ (v) = \sqrt{\frac{T}{\mu}}$

$\sf \implies v = \sqrt{ \frac{2.06 \times {10}^{4} }{0.175} }$

$\sf \implies v \approx \sqrt{11.77 \times {10}^{4} }$

$\sf \implies v \approx 3.43 \times {10}^{2}$

$\sf \implies v \approx 343 \: m/s$