Question

A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?

Answer 1

Speed of Wave is 32 m/s

Explanation:

Given,

Length of the steel wire = 64 cm

Weight = 5 g

Applied force = 8 N

Thus, we have:

Mass per unit length = $\frac {5}{64}$ gm/cm

Tension, T = 8 N

                  = $8 \times 10^5$dyn

Speed, v = $\sqrt \frac {T}{m}$

               = $\sqrt \frac {8 \times 10^5 \times 64}{5}$

               = 3200 cm/s  = 32 m/s

Answer 2

speed of a transverse wave $V = 32 \frac{m}{s}$

Exeplanation:

Given that,

Mass of the wire $m = \textrm{5 gram}$

$m = 5\times10^{-3}Kg$  

Length of the wire$l = \textrm{64 cm}$

$l = 64\times10^{-2} m$

Stretching force $f = \textrm{8 Netwon}$  

speed of a transverse wave passing is given by  

$V = \sqrt{\frac{f\times l}{m}}$

$V = \sqrt{\frac{8\times 64\times10^{-2}}{5\times10^{-3}}}$

$V = \sqrt{1024}$

$V = 32 \frac{m}{s}}$