A transverse harmonic wave on a string is described by $y = 3 \sin \,(36t + 0.018x + \frac{\pi}{4})$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between  two sucessive crests in the wave is .... $m$

A string of length $1\ m$ fixed at both ends is vibrating in $3^{rd}$ overtone. Tension in string is $200\ N$ and linear mass density is $5\ gm/m$ . Frequency of these vibrations is ..... $Hz$

The fundamental frequency of a sonometer wire of length $l$ is $n_0$ . A bridge is now introduced at a distance of $\Delta l ( < < l)$ from the centre of the wire. The lengths of wire on the two sides of the bridge are now vibrated in their fundamental modes. Then, the beat frequency nearly is

A transverse wave of frequency $500 \,Hz$ and speed $100 \,m / s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$, the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$, respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} s$ is ............ $m$

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by

$y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} - \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is  .... $N$

A string is rigidly tied at two ends and its equation of vibration is given by $y = \cos 2\pi \,t\sin \sin \pi x.$ Then minimum length of string is .... $m$