$A$ pipe open at both ends produces a note of frequency $f_1$. When the pipe is kept with $3/4$th of its length in water,it produces a note of frequency $f_2$. The ratio $f_1/f_2$ is

The lengths of two open organ pipes are $l$ and $(l + \Delta l)$ respectively. Neglecting end correction,the frequency of beats between them will be approximately (Here $v$ is the speed of sound).

$A$ closed organ pipe has a fundamental frequency $n$. If its length is doubled and its radius is halved,its fundamental frequency nearly becomes-

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now ..... $f$.

$A$ 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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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.)

Sound waves of frequency $660 \, Hz$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particle has maximum amplitude of vibration is .... $m$ (velocity of sound in air is $330 \, m/s$)