A string of length $1 \mathrm{~m}$ and mass $2 \times 10^{-5} \mathrm{~kg}$ is under tension $\mathrm{T}$. when the string vibrates, two successive harmonics are found to occur at frequencies $750 \mathrm{~Hz}$ and $1000 \mathrm{~Hz}$. The value of tension $\mathrm{T}$ is. . . . . . .Newton.

In the figure shown a mass $1\  kg$ is connected to a string of mass per unit length $1.2\  gm/m$ . Length of string is $1\  m$ and its other end is connected to the top of a ceiling which is accelerating up with an acceleration $2\  m/s^2$ . A transverse pulse is produced at the lowest point of string. Time taken by pulse to reach the top of string is .... $s$

Write equation of transverse wave speed for stretched string.

A steel wire has a length of $12.0 \;m$ and a mass of $2.10 \;kg .$ What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at $20\,^{\circ} C =343\; m s ^{-1}$

The transverse displacement of a string (clamped at its both ends) is given by

$y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$

where $x$ and $y$ are in $m$ and $t$ in $s$. The length of the string is $1.5\; m$ and its mass is $3.0 \times 10^{-2}\; kg$

Answer the following:

$(a)$ Does the function represent a travelling wave or a stationary wave?

$(b)$ Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?

$(c)$ Determine the tension in the string.

The extension in a string, obeying Hooke's law, is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5x$, the speed of sound will be