$A$ man can hear sounds in the frequency range $120 \, Hz$ to $12020 \, Hz$ only. He is vibrating a piano string having a tension of $240 \, N$ and a mass of $3 \, g$. The string has a length of $8 \, m$. How many different frequencies can he hear?

In a resonance tube experiment,the first and second resonance are heard when the water level is $24.1 \ cm$ and $74.1 \ cm$ respectively,below the open end of the tube. The inner diameter of the tube is (in $cm$)

The lengths of the two organ pipes open at both ends are $L$ and $(L+L_1)$. If they are sounded together,the beat frequency will be ($v=$ velocity of sound in air).

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In the resonance tube experiment,if the tuning fork is replaced by another identical tuning fork but with its arms filed,the length of the air column should be increased to obtain resonance again.
Statement $2:$ On filing the arms,the frequency of a tuning fork increases.

The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is $100 \ Hz$. The frequency of the third harmonic of the closed pipe is ..... $Hz$.

$A$ glass tube is open at both ends. $A$ tuning fork of frequency $f$ resonates with the air column inside the tube. Now,the tube is placed vertically inside water so that half the length of the tube is filled with water. Now,the air column inside the tube is in unison with another fork of frequency $f^{\prime}$. Then,