In a resonance tube experiment,two consecutive resonances are observed when the lengths of the air columns are $16 \ cm$ and $49 \ cm$. If the frequency of the tuning fork used is $500 \ Hz$,the velocity of sound in air is $... \ ms^{-1}$.

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

$A$ string fixed at both ends is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency $f_1$. Now,one end becomes free. If the frequency of the tuning fork is increased slowly from $f_1$,then again a resonance is obtained when the frequency is $f_2$. If in this case the string vibrates in the $n^{th}$ harmonic,then:

On producing waves of frequency $1000 \text{ Hz}$ in a Kundt's tube,the total distance between $6$ successive nodes is $85 \text{ cm}$. The speed of sound in the gas filled in the tube is ..... $m/s$.

An open pipe resonates with a tuning fork of frequency $500 \ Hz$. It is observed that two successive nodes are formed at distances $16 \ cm$ and $46 \ cm$ from the open end. The speed of sound in air in the pipe is ..... $m/s$.

The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is $100 \ Hz$. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is: (in $Hz$)