A 1 ; m long (both ends open) organ pipe is k | vedclass

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

Question

(B) The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$.Assuming $\gamma$ and $P$ are the same for the gas and air,we have $\fr

Vedclass · Accepted Answer

$106$

Vedclass · Answer

(B) The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma P}{ho}}$.Assuming $\gamma$ and $P$ are the same for the gas and air,we have $\frac{v_{gas}}{v_{air}} = \sqrt{\frac{ho_{air}}{ho_{gas}}}$.Given $ho_{gas} = 2 ho_{air}$,we get $\frac{v_{gas}}{300} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.Thus,$v_{gas} = \frac{300}{\sqrt{2}} = 150 \sqrt{2} \; m/s$.For an open organ pipe of length $L$,the fundamental frequency is $f_1 = \frac{v}{2L}$ and the second harmonic is $f_2 = \frac{2v}{2L} = \frac{v}{L}$.The frequency difference is $\Delta f = f_2 - f_1 = \frac{v}{2L}$.Substituting the values,$\Delta f = \frac{150 \sqrt{2}}{2(1)} = 75 \sqrt{2} \approx 75 	imes 1.414 = 106.05 \; Hz$.Rounding to the nearest integer,the answer is $106 \; Hz$.

$A$ $1 \; m$ long (both ends open) organ pipe is kept in a gas that has double the density of air at $STP$. Assuming the speed of sound in air at $STP$ is $300 \; m/s$,the frequency difference between the fundamental and second harmonic of this pipe is . . . . . . $Hz$.

Similar Questions

In a resonance tube experiment,two consecutive resonances are observed when the lengths of the air columns are $16 \ cm$ and $49 \ cm$. If the frequency of the tuning fork used is $500 \ Hz$,the velocity of sound in air is $... \ ms^{-1}$.

The second overtone of an open organ pipe $A$ and a closed pipe $B$ have the same frequency at a given temperature. It follows that the ratio of the

$A$ 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 $340\, m/s$)

In a pipe closed at one end,an air column is vibrating in the fourth overtone. How many nodes and antinodes does the vibrating air column have?

An organ pipe $P_1$ closed at one end has a vibrating air column in its first overtone,and another pipe $P_2$ open at both ends has a vibrating air column in the third overtone. Both are in resonance with a given tuning fork. The ratio of the length of pipe $P_1$ to that of $P_2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module