Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies $150 \,Hz$ and $250 \,Hz$. The fundamental frequency of the air column is: (in $\,Hz$)

The fundamental frequency of a closed pipe of length $L$ is equal to the second overtone of a pipe open at both the ends of length $(XL)$. The value of $X$ is (Neglect end correction).

What is the base frequency if a pipe gives notes of frequencies $425 \text{ Hz}, 255 \text{ Hz},$ and $595 \text{ Hz}$? Also,decide whether the pipe is closed at one end or open at both ends.

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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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

In a resonance tube of length $0.8 \,m$, an air column vibrates with a source of frequency $375 \,Hz$ for a certain height of water from the bottom of the tube. What is the water level corresponding to the fundamental frequency (in $\,m$)? (Neglect end correction, speed of sound in air = $330 \,m/s$)

An open pipe of length $33 \ cm$ resonates with a frequency of $1000 \ Hz$. If the speed of sound is $330 \ m/s$,then this frequency is: