Fundamental frequency of vibration of a string stretched between two rigid support is 50,Hz . mass o

English

Gujarati

Hindi

14.Waves and Sound

medium

The fundamental frequency of vibration of a string stretched between two rigid support is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g / m$. The speed of the transverse waves so produced in the string is $..........\,ms ^{-1}$

A

$90$

B

$45$

C

$30$

D

$15$

(JEE MAIN-2023)

Solution

Fundamental frequency $=50\,Hz$

$\frac{mass}{length}$=$\frac{20 g}{m}$

mass$=18\,g$

length of string $=\frac{18}{20} m =\frac{9}{10} m$

from diagram $\frac{\lambda}{2}=\ell$

$\Rightarrow \lambda=2 \ell=\frac{9}{5}\,m$

again speed $v=f \lambda=50 \times \frac{9}{5}=90\,m / s$

Standard 11

Physics

Share

Similar Questions

A string of length $2 m$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 Hz$ then the waves would travel on its with a velocity of ….. $m/s$

medium

A sonometer wire oflength $1.5\ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 $ $kg/m^3$ and $2.2 \times 10^{11}$ $N/m^2$ respectively?

medium

(JEE MAIN-2013)

The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$ where $x$ and $y$ are in centimetre and $t$ in second. The separation between two adjacent nodes is …. $cm$

medium

A string $1\,\,m$ long is drawn by a $300\,\,Hz$ vibrator attached to its end. The string vibrates in $3$ segments. The speed of transverse waves in the string is equal to …. $m/s$

medium

The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be ……… $\%$

medium