$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

$A$ transverse displacement of a vibrating string is given by $y = 0.06 \sin \left( \frac{2 \pi}{3} x \right) \cos (120 \pi t)$. If the mass per unit length of the string is $4 \times 10^{-2} \ kg/m$,then the tension in the string will be: (in $N$)

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$. Here $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is: (in $cm$)

$A$ stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1$ (figure). At an instant,this particle is at its mean position and is moving towards its negative extreme. Which of the following sets of particles are in the same phase as particle $1$?

The vibration of a string fixed at both ends is described by $Y = 2 \sin(\pi x) \sin(100\pi t)$,where $Y$ is in $mm$,$x$ is in $cm$,and $t$ is in $sec$. Then:

$A$ string fixed at both its ends vibrates in $5$ loops as shown in the figure. The total number of nodes and antinodes are respectively: