A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y(x$, $t )=(0.01 \ m ) \sin \left[\left(62.8 \ m ^{-1}\right) x \right] \cos \left[\left(628 s ^{-1}\right) t \right]$. Assuming $\pi=3.14$, the correct statement$(s)$ is (are) :

$(A)$ The number of nodes is $5$ .

$(B)$ The length of the string is $0.25 \ m$.

$(C)$ The maximum displacement of the midpoint of the string its equilibrium position is $0.01 \ m$.

$(D)$ The fundamental frequency is $100 \ Hz$.

Mechanical waves on the surface of a liquid are

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.

A uniform string oflength $20\ m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is (take $g= 10 $ $ms^{-2}$ )

Figure here shows an incident pulse $P$ reflected from a rigid support. Which one of $A, B, C, D$ represents the reflected pulse correctly

A transverse wave is passing through a string shown in figure. Mass density of the string is $1 \ kg/m^3$ and cross section area of string is $0.01\ m^2.$ Equation of wave in string is $y = 2sin (20t - 10x).$ The hanging mass is (in $kg$):-