The equation of a stationary wave is $ y = 2 \sin \left( \frac{\pi x}{15} \right) \cos (48 \pi t) $. The distance between a node and its next antinode is (in $units$)

The equation of a standing wave in a string fixed at both ends is given as $y = 2A \sin kx \cos \omega t$. The amplitude and frequency of a particle vibrating at the midpoint between an antinode and a node are respectively:

Standing waves are produced in a string $16 \ m$ long. If there are $9$ nodes between the two fixed ends of the string and the speed of the wave is $32 \ m/s$,what is the frequency of the wave (in $Hz$)?

When a stationary wave is formed,what is its frequency compared to the individual waves that form it?

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

$A$ 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 $N$)