The fundamental frequency of a sonometer wire increases by $6 \mathrm{Hz}$ if its tension is increased by $44 \%$ keeping the length constant. Find the change in the fundamental frequency of the sonometer when the length of the wire is increased by $20 \%$ keeping the original tension in the wire.

Find velocity of wave in $\left(\mathrm{m} {\mathrm{s}}^{-1}\right)$ in string $A$ and $B$.

The length of a sonometer wire is $1.21 \mathrm{m}$. Find the length of the three segments for fundamental frequencies to be in the ratio $1 : 2 : 3$.

In the figure shown $A$ and $B$ are two ends of a string of length $100 \mathrm{m}.\mathit{ }{S}_1$ and $S_2$ are two sources due to which points $‘A’$ and $‘B’$ oscillate in $‘y’$ and $‘z’$ directions respectively according to the equation $y=2\sin (100\mathrm{\pi }t+30°)$ and $z=3\sin (100\pi t+60°)$ where $t$ is in $\sec$ and $y$ is in $\mathrm{mm}$. The speed of propagation of disturbance along the string is $50 \mathrm{m} {\mathrm{s}}^{-1}$. Find the instantaneous position vector (in $\mathrm{mm}$) and velocity vector in $(\mathrm{m} {\mathrm{s}}^{-1})$ of a particle $‘P’$ of string which is at $25 \mathrm{m}$ from $A$. You have to find these parameters after both the disturbances from $S_1$ and $S_2$ have reached $‘P’$. Also find the phase difference between the waves at the point $‘P’$ when they meet at $‘P’$ first time.