Calculate frequency of second harmonic formed on a string of length 0.5 m and mass 2 × 10

English

Gujarati

Hindi

14.Waves and Sound

medium

Calculate the frequency of the second harmonic formed on a string of length $0.5 m$ and mass $2 × 10^{-4}$ kg when stretched with a tension of $20 N$ .... $Hz$

A

$274.4$

B

$744.2$

C

$44.72$

D

$447.2 $

Solution

(d) Mass per unit length $m = \frac{{2 \times {{10}^{ – 4}}}}{{0.5}}kg/m$

$ = 4 \times {10^{ – 4}}kg/m$

Frequency of $2^{nd}$ harmonic ${n_2} = 2{n_1}$

$ = 2 \times \frac{1}{{2l}}\sqrt {\frac{T}{m}} $$ = \frac{1}{{0.5}}\sqrt {\frac{{20}}{{4 \times {{10}^{ – 4}}}}} = 447.2Hz$

Standard 11

Physics

Share

Similar Questions

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by

$y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} – \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is …. $N$

hard

(AIEEE-2010)

Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is $1 : 4 : 9 : 16$ then the ratio of their fundamental frequencies are

easy

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$…..$

medium

(JEE MAIN-2020)

Unlike a laboratory sonometer, a stringed instrument is seldom plucked in the middle. Supposing a sitar string is plucked at about $\frac{1}{4}$th of its length from the end. The most prominent harmonic would be

easy

The fundamental frequency of a sonometer wire increases by $6$ $Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$, keeping the original tension in the wire will be :-

hard