The equation of a longitudinal wave is represented as $y = 20 \cos \pi (50t - x)$. Its wavelength is ..... $cm$.

The equation of a wave is given by (all quantities expressed in $M.K.S.$ units) $Y = 5 \sin(10\pi t - 0.1\pi x)$ along the $x$-axis. The phase difference between two points separated by a distance of $10 \ m$ along the $x$-axis is:

When a wave travels in a medium,the particle displacement is given by $y = a \sin(2 \pi (bt - cx))$,where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

$A$ wave travelling in the positive $x-$direction with amplitude $A = 0.2\;m$ has a velocity of $v = 360\;m/s.$ If the wavelength $\lambda = 60\;m,$ then the correct expression for the wave is:

The equation of a progressive wave is $y = 8 \sin \left[ \pi \left( \frac{t}{10} - \frac{x}{4} \right) + \frac{\pi}{3} \right]$. The wavelength of the wave is .... $m$.

$A$ triangular pulse moving at $2 \ cm/s$ on a rope approaches an end at which it is free to slide on a vertical pole. What is the particle speed at the free end at $\frac{3}{4} \ s$ from the instant shown? (in $cm/s$)