A string of length $1\,\,m$ and linear mass density $0.01\,\,kgm^{-1}$ is stretched to a tension of $100\,\,N.$ When both ends of the string are fixed, the three lowest frequencies for standing wave are $f_1, f_2$ and $f_3$. When only one end of the string is fixed, the three lowest frequencies for standing wave are $n_1, n_2$ and $n_3$. Then

The frequency of a tuning fork is $256\, Hz$. The velocity of sound in air is $344\, ms^{-1}$. The distance travelled (in $meters$) by the sound during the time in which the tunning fork complete $32$ vibrations is

Two wires are producing fundamental notes of the same frequency. Change in which of the following factors of one wire will not produce beats between them

A string fixed at one end is vibrating in its second overtone. The length of the string is $10\ cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is

A wire of length $30\,cm$, stretched between rigid supports, has it's $n^{\text {th}}$ and $(n+1)^{\text {th}}$ harmonics at $400\,Hz$ and $450\; Hz$, respectively. If tension in the string is $2700\,N$, it's linear mass density is………$kg/m$.