The fundamental note produced by a closed organ pipe is of frequency $f$. The fundamental note produced by an open organ pipe of the same length will be of frequency .... $(f)$

The frequency of the second overtone of an open pipe is equal to the frequency of the first overtone of a closed pipe. The ratio of the lengths of the open pipe to the closed pipe is

$A$ tuning fork produces four beats per second with two open organ pipes having lengths $30 \ cm$ and $31 \ cm$. Find the frequency of the tuning fork in $Hz$.

In the fundamental mode,the time required for a sound wave to reach the closed end of a pipe filled with air is $t$ seconds. The frequency of vibration of the air column is:

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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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

$A$ whistle whose air column is open at both ends has a fundamental frequency of $5100 \ Hz$. If the speed of sound in air is $340 \ ms^{-1}$,the length of the whistle,in $cm$,is