A tuning fork with frequency $800 \mathrm{Hz}$ produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at lengths $9.75 \mathrm{cm},31.25 \mathrm{cm}$ and $52.75 \mathrm{cm}$. The speed of sound in air is

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27°\mathrm{C}$, two successive resonances are produced at $20$ $ \mathrm{cm}$ and $73$ $\mathrm{cm}$ of column length. If the frequency of the tuning fork is $320$ $ \mathrm{Hz}$, the velocity of sound in air at $27°\mathrm{C}$ is,

Three sound waves of equal amplitudes have frequencies $(n-1)$, $n$, $(n+1)$. They superimpose to give beats. The number of beats produced per second will be 

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50 \mathrm{cm}$. The next larger length of the column resonating with the same tuning fork is

A source of sound $S$ emitting waves of frequency $100 \mathrm{Hz}$ and an observer $\mathrm{O}$ are located at some distance from each other. The source is moving with a speed of $19.4 \mathrm{m}{ \mathrm{s}}^{-1}$ at an angle of $60°$with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330{ \mathrm{m} \mathrm{s}}^{-1}$ ), is

The fundamental frequency of a closed organ pipe of length $20 \mathrm{cm}$ is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

If $n_1, n_2, n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by