In a simple harmonic wave,the minimum distance between particles in the same phase always having the same speed is ..........

When a wave enters into a rarer medium from a denser medium,the property of the wave which remains constant is

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

$A$ transverse wave in a medium is given by $y = A \sin 2(\omega t - kx)$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to the magnitude of the wave velocity. What is the value of $A$?

You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-vt$ or $x+vt$,i.e.,$y=f(x \pm vt)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave:
$(a)$ $(x-vt)^2$
$(b)$ $\log[(x+vt)/x_0]$
$(c)$ $1/(x+vt)$

$A$ person is producing a wave in a string by moving his hand first up and then down. If the frequency is $\frac{1}{8} \, Hz$,then find out the time taken by a particle which is at a distance of $9 \, m$ from the source to move to the lower extreme for the first time in seconds. (Given $\lambda = 24 \, m$)