The vibrations of four air columns are shown | vedclass

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

Question

(D) For figure $(a)$,$L = \frac{\lambda_1}{4} \Rightarrow \lambda_1 = 4L$.For figure $(b)$,$L = \frac{\lambda_2}{4} + \frac{\lambda_2}{2} + \frac{\lam

Vedclass · Accepted Answer

$1$:$4$:$2$:$3$

Vedclass · Answer

(D) For figure $(a)$,$L = \frac{\lambda_1}{4} \Rightarrow \lambda_1 = 4L$.For figure $(b)$,$L = \frac{\lambda_2}{4} + \frac{\lambda_2}{2} + \frac{\lambda_2}{4} = \lambda_2 \Rightarrow \lambda_2 = L$.For figure $(c)$,$L = \frac{\lambda_3}{4} + \frac{\lambda_3}{4} + \frac{\lambda_3}{2} = \lambda_3 \Rightarrow \lambda_3 = L$ (Note: Based on the diagram,it represents a pipe open at both ends with one node in the middle,so $L = \lambda_3/2 \Rightarrow \lambda_3 = 2L$).For figure $(d)$,$L = \frac{\lambda_4}{2} + \frac{\lambda_4}{4} = \frac{3\lambda_4}{4} \Rightarrow \lambda_4 = \frac{4L}{3}$.Since frequency $f \propto \frac{1}{\lambda}$,we have $f_1 : f_2 : f_3 : f_4 = \frac{1}{\lambda_1} : \frac{1}{\lambda_2} : \frac{1}{\lambda_3} : \frac{1}{\lambda_4}$.Substituting the values: $f_1 : f_2 : f_3 : f_4 = \frac{1}{4L} : \frac{1}{L} : \frac{1}{2L} : \frac{3}{4L}$.Multiplying by $4L$,we get $1 : 4 : 2 : 3$.

The vibrations of four air columns are shown below. The ratio of frequencies is

Similar Questions

In the fundamental mode,the time required for a sound wave to reach the closed end of an air-filled pipe is $t$ seconds. What is the frequency of vibration of the air column?

Explain the formation of stationary waves in a closed pipe and derive the equations for natural frequencies (normal modes).

$A$ tuning fork vibrates with frequency $256\, Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe in $cm$? (Speed of sound in air is $340\, m/s$)

$A$ closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?

$A$ whistle whose air column is open at both ends has a fundamental frequency of $5100 \ Hz$. If the speed of sound in air is $340 \ ms^{-1}$,the length of the whistle,in $cm$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module