In the resonance tube experiment,the first resonant length is $l_1$ and the second resonant length is $l_2$. Then,the third resonant length will be:

At a temperature of $27^{\circ} C$, two identical organ pipes produce notes of frequency $140 \,Hz$. If the temperature of one pipe is raised to $57.75^{\circ} C$, then the number of beats produced per second is

$A$ student is experimenting with a resonance tube apparatus in a Physics lab to find the speed of sound at room temperature. He obtained the first two resonating lengths of the air column as $17 \, cm$ and $51 \, cm$,using a tuning fork of frequency $512 \, Hz$. Find the speed of sound at room temperature in $m/s$.

$A$ taut string fixed at both ends vibrates in its $n^{th}$ overtone. The distance between adjacent Node and Antinode is found to be $d$. If the length of the string is $L$,then:

The fundamental frequency of a closed pipe is $400 \text{ Hz}$. If $\left(\frac{1}{3}\right)^{rd}$ length of the pipe is filled with water, the frequency of the $2^{\text{nd}}$ harmonic of the pipe will be (Neglect end correction). (in $\text{ Hz}$)

$A$ pipe $20 \; cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430 \; Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is $340 \; m/s$).