The transverse displacement of a string of a linear density $0.01 \text{ kg m}^{-1}$,clamped at its ends is given by $Y_{(x, t)} = 0.03 \sin \left(\frac{2 \pi x}{3}\right) \cos (60 \pi t)$,where $x$ and $y$ are in metres and time $t$ is in seconds. The tension in the string is: (in $\text{ N}$)

Explain the reflection of a wave at a free support.

$A$ wave represented by the equation $y = A \cos (kx - \omega t)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation of the other wave is:

$A$ stationary wave is represented by $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between two consecutive nodes is (in $cm$)

$Assertion :$ For the formation of stationary waves,the medium must be bounded having definite boundaries.
$Reason :$ In the stationary wave,some particles of the medium remain permanently at rest.

The transverse displacement of a string (clamped at 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 $t$ is 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.