Question

(b) A sitar wire is under tension 30N and the length of the bridges is 80 cm. A 10m
sample of that wire has mass 2.2 g. Find the speed of transverse waves on the wire and the
fundamental frequency.(4)​

Answer 1

The speed of transverse waves on the wire is 369.3 m/s and the  fundamental frequency is 230.8 Hz

Explanation:

As we know that the speed of transverse wave in a straight wire is given as

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

where ${\mu}}$ is Mass per unit length and

T is tension

Here we know that

T = mg

A sitar wire is under tension 30N So, T = 30 N

Given, Mass of the wire = 2.2 g

Length of the wire = 10m

We know that

$\mu = \frac{m}{L}$  where m is Mass of the string and L is Length of the string,

$\mu = \frac{2.2 \times 10^{-3}}{10}$

now we have

$v = \sqrt{\frac{30 \times 10}{2.2\times 10^{-3}}}$

v = 369.3 m/s

Now fundamental frequency of the wire is given as

$f_o = \frac{v}{2L}$

here the length where wave forms is given as

L = 80 cm

Thus we have

$f_o = \frac{369.3}{2(0.80)}$

$f_o$ = 230.8 Hz

Hence, the speed of transverse waves on the wire is 369.3 m/s and the  fundamental frequency is 230.8 Hz