$A$ string of length $3 \ m$ and linear mass density $0.0025 \ kg/m$ is fixed at both ends. One of its resonance frequencies is $252 \ Hz$. The next higher resonance frequency is $336 \ Hz$. Then the fundamental frequency will be ..... $Hz$.

The fundamental frequency of an air column in a pipe closed at one end is $150 \ Hz$. If the same pipe is open at both ends,the frequencies produced in $Hz$ are:

$A$ person blows into the open end of a long pipe. As a result,a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe:

$A$ student is performing the experiment of a resonance column. The diameter of the column tube is $6 \, cm$. The frequency of the tuning fork is $504 \, Hz$. The speed of sound at the given temperature is $336 \, m/s$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is..........$cm$.

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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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

An open air pipe of length $80 \,cm$ has the second harmonic frequency equal to the fundamental frequency of a closed organ air pipe. The length of the closed pipe is (in $\,cm$)