A pipe closed at one end produces a fundamental note of $412\,Hz.$  It is cut into two pieces of equal length the fundamental notes produced by the two pieces are

A wire of density $9 \times 10^3 \,kg/m^3$ is stretched between two clamps one meter  apart and is subjected to an extension of $4.9 \times 10^{-4} \,m$. What will be the  lowest frequency of the transverse vibrations in the wire ... $Hz$ $[Y = 9 \times 10^{10} \,N/m^2]$ ?

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 guitar string of length $90\,cm$ vibrates with a fundamental frequency of $120\,Hz.$ The length of the string producing a fundamental frequency of $180\,Hz$ will be $...........cm$.

The length of the wire shown in figure between the pulleys is $1.5\, m$ and its mass is  $12.0\,g$. The frequency of vibration with which the wire vibrates in three loops forming antinode at the mid point of the wire is $(g = 9.8 \,m/s^2)$

A sine wave of wavelength $\lambda $ is travelling in a medium. The minimum distance between the two particles, always having same speed, is