The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$ where $x$ and $y$ are in centimetre and $t$ in second. The separation between two adjacent nodes is …. $cm$

The tension in a piano wire is $10N$. What should be the tension in the wire to produce a note of double the frequency …. $N$

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 … $Hz$ $[Y = 9 \times 10^{10} \,N/m^2]$ ?

A string $2.0\, m$ long and fixed at its end is driven by a $240\, Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

Transverse waves of same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B$. The ratio of velocities of wave in $A$ and $B$ is