The frequency of a stretched uniform wire und | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the initial tension in the wire be $T$ and the mass per unit length be $m$. The frequency of the stretched wire is given by $f_w = \frac{1}{2L

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the initial tension in the wire be $T$ and the mass per unit length be $m$. The frequency of the stretched wire is given by $f_w = \frac{1}{2L_w} \sqrt{\frac{T}{m}}$.The fundamental frequency of a closed organ pipe of length $L_p$ is $f_c = \frac{v}{4L_p}$.According to the problem,initially,$f_w = f_c$,so $\frac{1}{2L_w} \sqrt{\frac{T}{m}} = \frac{v}{4L_p}$ ..... $(i)$.When the tension is increased by $8 \ N$,the new frequency is $f_w' = \frac{1}{2L_w} \sqrt{\frac{T+8}{m}}$. This is in resonance with the first overtone of the closed pipe,which is $3f_c = \frac{3v}{4L_p}$.So,$\frac{1}{2L_w} \sqrt{\frac{T+8}{m}} = \frac{3v}{4L_p}$ ..... $(ii)$.Dividing equation $(i)$ by equation $(ii)$,we get:$\frac{\sqrt{T}}{\sqrt{T+8}} = \frac{1}{3}$.Squaring both sides:$\frac{T}{T+8} = \frac{1}{9}$.$9T = T + 8 \Rightarrow 8T = 8 \Rightarrow T = 1 \ N$.

The frequency of a stretched uniform wire under tension is in resonance with the fundamental frequency of a closed tube. If the tension in the wire is increased by $8 \ N$,it is in resonance with the first overtone of the closed tube. The initial tension in the wire is .... $N$.

Similar Questions

The length,tension,diameter,and density of a wire $B$ are double those of the corresponding quantities for another stretched wire $A$. Then:

$Assertion :$ The pitch of wind instruments rises and that of string instruments falls as an orchestra warms up.
$Reason :$ When temperature rises,the speed of sound increases,but the speed of a wave in a string fixed at both ends decreases.

If $T$ is the reverberation time of an auditorium of volume $V$,then:

Diffraction of sound waves is more evident than light waves in daily life because:

Vedclass Test Series

Exam Paper Generator

Online Exam Module