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

The lengths of the two organ pipes open at both ends are $L$ and $(L+L_1)$. If they are sounded together,the beat frequency will be ($v=$ velocity of sound in air).

$A$ student is performing the Resonance Column experiment. The diameter of the column tube is $4 \ cm$. The frequency of the tuning fork is $512 \ Hz$. The air temperature is $38^{\circ} C$,at which the speed of sound is $336 \ m/s$. The zero of the meter scale coincides with the top end of the resonance column. When the first resonance occurs,the reading of the water level in the column is: (in $cm$)

While measuring the speed of sound by performing a resonance column experiment,a student gets the first resonance condition at a column length of $18 \ cm$ during winter. Repeating the same experiment during summer,she measures the column length to be $x \ cm$ for the second resonance. Then

The fundamental frequency of a pipe is $100 \ Hz$ and the next two frequencies are $300 \ Hz$ and $500 \ Hz$. Then:

An open and a closed organ pipe have the same length. The ratio of the $p^{th}$ mode of frequency of vibration of the two pipes is