Question

A wire of the length 0.5 m is stretched by a weight of 2 kg. If the mass per unit length of the wire is 1.96 ×

10-3

kg/m, find the fundamental frequency of the wire and frequency of its first overtone.​

Answer 1

The fundamental frequency of wire is 100 Hz

Frequency of first overtone is 200 Hz

Explanation:

Length of the wire $l=0.5$ m

Weight attached $=2$ kg

Therefore, tension in the wire

$T=2g$ N

Mass per unit length $m=1.96\times 10^{-3}$ kg/m

We know that fundamental frequency of vibration is given by

$\nu=\frac{1}{2l}\sqrt{\frac{T}{m}}$

$\implies \nu=\frac{1}{2\times0.5}\sqrt{\frac{2\times 9.8}{1.96\times 10^{-3}}}$

$\implies \nu=\sqrt{\frac{19.6}{1.96\times 10^{-3}}}$

$\implies \nu=\sqrt{\frac{1.96\times 10}{1.96\times 10^{-3}}}$

$\implies \nu=\sqrt{10^4}$ s⁻¹

$\implies \nu=100$ Hz

Frequency of first overtone

$=2\nu$

$=2\times 100$

$=200$ Hz

Hope this answer is helpful.

Know More:

Q: Illustrate using labelled diagrams only, a sonometer wire of length, l, vibrating at its(i) fundamental(ii) first overtone(iii) second overtone.

Click Here: https://brainly.in/question/737718

Q: A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100Hz. Determine the linear density of material of wire. (Ans : 0.0049 kg/m)

Click Here: https://brainly.in/question/7000086

Answer 2

Given :

The length of wire , l = 0.5 m

Weight  = 2 kg

Mass per unit , μ = 1.96 x 10 ^ (-3)

To find :

Fundamental frequency and frequency of the first overtone .

Solution :

Tension , T = mass * g

                   = 2 * 9.8

                   = 19.6 N

fundamental frequency , v = ( 1 / 2*l ) * √( T / μ )

                                            = ( 1 / 1 ) * √( 19.6 / 1.96 x 10 ^ (-3) )

                                            = √10000

                                            = 100 Hz

frequency of first overtone = 2 * fundamental frequency

                                             = 2 * 100 Hz

                                             = 200 Hz

The fundamental frequency is 100Hz and the frequency of the first overtone is 200 Hz .