Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave
$y = 2\,cos\,(3x)\,sin\,(10t)$
$y = 2\,\sqrt {x - vt}$
$y = 3\,sin\,(5x -0.5t) + 4\,cos\,(5x -0.5t)$
$y = cos\,x\,sin\,t + cos\,2x\,sin\,2t$
Calculate the temperature at which the speed of sound will be two times its ..... $K$ value at $0\,^oC$
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
Two tuning forks $A$ and $B$ produce $8\, beats/s$ when sounded together. $A$ gas column $37.5\, cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks, are
Which of the following is correct ?
A wave travelling along the $x- $ axis is described by the equation $y(x, t) = 0.005\,\,cos(\alpha x\,-\,\beta t).$ If the wavelength and the time period of the wave are $0.08 \,\,m$ and $2.0\,\,s,$ respectively, then $\alpha $ and $\beta $ in appropriate units are