The equation of a simple harmonic wave produced in a string under a tension of $0.4 \,N$ is given by $y=4 \sin (3x+60t) \,m$. The mass per unit length of the string is:

As shown in the figure, a block of mass $9 \, kg$ is hung by a wire of area of cross-section $1 \, mm^2$ in a lift going up with an acceleration of $2 \, ms^{-2}$. If the speed of the transverse wave on the wire is $120 \, ms^{-1}$, the density of the material of the wire is (Acceleration due to gravity $= 10 \, ms^{-2}$)

$A$ string of $7 \; m$ length has a mass of $0.035 \; kg$. If the tension in the string is $60.5 \; N$,then the speed of a wave on the string is .... $m/s$.

$A$ string of mass $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

$A$ wire of linear mass density $\mu = 10^{-2} \, kg \, m^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of the wire such that $m$ rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 \, m \, s^{-1}$.

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).