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

A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = young’s modulus, $\rho$ = density, $\alpha$ = coefficient of linear expansion) then the frequency of transverse vibration is proportional to : 

A standing wave exists in a string of length $150\ cm$ , which is fixed at both ends with rigid supports . The displacement amplitude of a point at a distance of $10\ cm$ from one of the ends is $5\sqrt 3\ mm$ . The nearest distance between the two points, within the same loop and havin displacment amplitude equal to $5\sqrt 3\  mm$ is $10\ cm$ . Find the maximum displacement amplitude of the particles in the string .... $mm$

A pipe $20$ $\mathrm{cm}$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5$ $\mathrm{Hz}$ ?( sound velocity in air $= 330$ $\mathrm{m/s}$ ).

A light wave travels through three transparent materials of equal thickness. Rank in order, from the highest to lowest, the indices of refraction $n_1, n_2$ and $n_3$.

A tuning fork vibrating with a sonometer having a wire of length $20 \,cm$ produces $5$ beats per second. The beats frequency does not change if the length of the wire is changed to $21 \,cm$. The frequency of the tuning fork must be ............ $Hz$