A string fixed at one end and free at the oth | vedclass

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

Question

(B) For a string fixed at one end and free at the other,the length $L$ is given by $L = (2n+1) \frac{\lambda}{4}$,where $n$ is the overtone number.For

Vedclass · Accepted Answer

$\sqrt{2} \ mm$

Vedclass · Answer

(B) For a string fixed at one end and free at the other,the length $L$ is given by $L = (2n+1) \frac{\lambda}{4}$,where $n$ is the overtone number.For the second overtone,$n = 2$,so $L = 5 \frac{\lambda}{4}$.Given $L = 10 \ cm$,we have $10 = \frac{5 \lambda}{4}$,which gives $\lambda = 8 \ cm$.The amplitude $A(x)$ at a distance $x$ from the fixed end is given by $A(x) = A_{max} \sin(kx)$,where $k = \frac{2\pi}{\lambda}$.Here $A_{max} = 2 \ mm$ and $x = 9 \ cm$.$A(9) = 2 \sin\left(\frac{2\pi}{8} 	imes 9ight) = 2 \sin\left(\frac{9\pi}{4}ight) = 2 \sin\left(2\pi + \frac{\pi}{4}ight) = 2 \sin\left(\frac{\pi}{4}ight)$.$A(9) = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2} \ mm$.

$A$ string fixed at one end and free at the other is vibrating in its second overtone. The length of the string is $10 \ cm$ and the maximum amplitude of vibration of particles of the string is $2 \ mm$. Then the amplitude of the particle at $9 \ cm$ from the fixed end is

Similar Questions

The figure shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ among $1, 2,$ and $3$ are in phase with point $X$?

$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

In a standing wave on a string rigidly fixed at both ends:

$A$ standing wave pattern is formed on a string. One of the waves is given by the equation $y_1 = a \cos(\omega t - kx + \pi/3)$. Find the equation of the other wave such that at $x = 0$,a node is formed.

The equation of a stationary wave is $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$. The distance between two consecutive nodes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module