A wire of density $9 \times 10^3 kg /m^3$ is stretched between two clamps $1 m$ apart and is subjected to an extension of $4.9 \times 10^{-4} m$. The lowest frequency of transverse vibration in the wire is ..... $Hz$ ($Y = 9 \times 10^{10} N / m^2$)

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequecny of the new pipe so obtained will be

A stretched string of length $l,$ fixed at both ends can sustain stationary waves of wavelength $\lambda ,$ given by

A hollow pipe of length $0.8 \mathrm{~m}$ is closed at one end. At its open end a $0.5 \mathrm{~m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \mathrm{~N}$ and the speed of sound is $320 \mathrm{~ms}^{-1}$, the mass of the string is

The fundamental frequency of a string stretched with a weight of $4 kg$ is $256 Hz$. The weight required to produce its octave is .... $kg \,wt$

A clamped string is oscillating in $n^{th}$ harmonic, then