The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$

A uniform rope of mass $6\,kg$ hangs vertically from a rigid support. A block of mass $2\,kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\,m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top is (in $m$ )

Obtain the equation of speed of transverse wave on tensed (stretched) string.

Speed of a transverse wave on a straight wire (mass $6.0\; \mathrm{g}$, length $60\; \mathrm{cm}$ and area of cross-section $1.0\; \mathrm{mm}^{2}$ ) is $90\; \mathrm{ms}^{-1} .$ If the Young's modulus of wire is $16 \times 10^{11}\; \mathrm{Nm}^{-2},$ the extension of wire over its natural length is

The mass per unit length of a uniform wire is $0.135\, g / cm$. A transverse wave of the form $y =-0.21 \sin ( x +30 t )$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x \times 10^{-2} N$. Value of $x$ is . (Round-off to the nearest integer)

A copper wire is held at the two ends by rigid supports. At $50^{\circ} C$ the wire is just taut, with negligible tension. If $Y=1.2 \times 10^{11} \,N / m ^2, \alpha=1.6 \times 10^{-5} /{ }^{\circ} C$ and $\rho=9.2 \times 10^3 \,kg / m ^3$, then the speed of transverse waves in this wire at $30^{\circ} C$ is .......... $m / s$