A transverse wave is described by the equation $y = {y_0}\,\sin \,2\pi \,\left[ {ft - \frac{x}{\lambda }} \right]$ . The maximum particle velocity is equal to four times the wave velocity if

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda _2$ . The ratio $\lambda _2/\lambda _1$ is

The two waves represented by $y_1 = a\,sin(\omega\,t)$ and $y_2 = b\, cos\, (\omega\, t)$ have a phase difference of

A wave travelling along the $x-$ axis is described by the equation $y \,(x, t ) = 0.005\, cos \,\left( {\alpha x - \beta t} \right)$. If the wavelength and the time period of the wave are $0.08\,m$ and $2.0\, s$ respectively then $a$ and $b$ in appropriate units are

A string of mass $2.5\ kg$ is under a tension of $200\ N$ . The length of the stretched string is $20.0\ m$ . If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in .... $\sec$

If $L_1$ and $L_2$ are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is