A string is clamped at both ends and it is vi | vedclass

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

Question

(B) For a string clamped at both ends,the length $\ell$ in the $n^{th}$ harmonic is given by $\ell = n \frac{\lambda}{2}$.Given $n = 4$,we have $\ell

Vedclass · Accepted Answer

$80$

Vedclass · Answer

(B) For a string clamped at both ends,the length $\ell$ in the $n^{th}$ harmonic is given by $\ell = n \frac{\lambda}{2}$.Given $n = 4$,we have $\ell = 4 \frac{\lambda}{2} = 2\lambda$.The general equation of a stationary wave is $Y = A \sin(kx) \cos(\omega t)$,where $k = \frac{2\pi}{\lambda}$.Comparing the given equation $Y = 0.3 \sin(0.157 x) \cos(200\pi t)$ with the general form,we get $k = 0.157$.Since $0.157 \approx \frac{\pi}{20}$,we have $\frac{2\pi}{\lambda} = \frac{\pi}{20}$.Solving for $\lambda$,we get $\lambda = 40 \, m$.Substituting this into the length formula: $\ell = 2 \lambda = 2 	imes 40 = 80 \, m$.

$A$ string is clamped at both ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y = 0.3 \sin(0.157 x) \cos(200\pi t)$. The length of the string is ..... $m$ (all quantities are in $SI$ units).

Similar Questions

The fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled while keeping the tension constant,what is the new fundamental frequency?

$A$ string is divided into three segments such that the segments possess fundamental frequencies in the ratio $1: 2: 3$. Then,the lengths of the segments are in the ratio:

The fundamental frequency of a string stretched with a weight of $4 \ kg$ is $256 \ Hz$. The weight required to produce its octave is .... $kg \ wt$.

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$, the ratio of the lengths of the strings is :

$A$ string of length $1 \, m$ fixed at both ends is vibrating in the $3^{rd}$ overtone. The tension in the string is $200 \, N$ and the linear mass density is $5 \, g/m$. The frequency of these vibrations is ..... $Hz$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module