$A$ 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:

$A$ student is performing an experiment using a resonance column and a tuning fork of frequency $244 \ s^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350 \pm 0.005) \ m$,the gas in the tube is. (Useful information: $\sqrt{167 RT} = 640 \ J^{1/2} \ mol^{-1/2}$; $\sqrt{140 RT} = 590 \ J^{1/2} \ mol^{-1/2}$. The molar masses $M$ in grams are given in the options. Take the value of $\sqrt{\frac{10}{M}}$ for each gas as given there.)

$A$ closed pipe of length $300 \,cm$ contains some sand. $A$ speaker is connected at one of its ends. The frequency of the speaker at which the sand will arrange itself in $20$ equidistant piles is close to .......... $kHz$ (velocity of sound is $300 \,m/s$).

In the fundamental mode,the time taken by the wave to reach the closed end of an air-filled pipe is $0.01 \ s$. The fundamental frequency is (in $Hz$)

$A$ closed organ pipe $150 \ cm$ long gives $7$ beats per second with an open organ pipe of length $350 \ cm$,both vibrating in fundamental mode. The velocity of sound is . . . . . . $m/s$.

If the temperature increases,then what happens to the frequency of the sound produced by the organ pipe?