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

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse wave of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the wave when it reaches the top of the rope is $\lambda_2$. The ratio $\frac{\lambda_1}{\lambda_2}$ is

Two strings $A$ and $B$ of the same material are stretched by the same tension. The radius of string $A$ is double the radius of string $B$. $A$ transverse wave travels on string $A$ with speed $V_A$ and on string $B$ with speed $V_B$. The ratio $\frac{V_A}{V_B}$ is:

$A$ 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 .......... $m/s$.

The equation of a wave on a string of linear mass density $0.04 \ kg \ m^{-1}$ is given by $y = 0.02 \sin \left[ 2\pi \left( \frac{t}{0.04 \ s} - \frac{x}{0.50 \ m} \right) \right] \ m$. The tension in the string is .... $N$.

The linear mass density of a vibrating string is $1.3 \times 10^{-4} \ kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $y = 0.021 \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is approximately: (in $N$)