A uniform rope of length $10 \mathrm{m}$ and mass $3 \mathrm{kg}$ hangs vertically from a rigid support. A block of mass $1 \mathrm{kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.05 \mathrm{m}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

The phase difference between the following two waves $y_2$ and $y_1$ is:

$y_1=a\sin \left(\omega t-kx\right)$

$y_2=b\cos \left(\omega t-kx+\frac{\pi }{3}\right)$

The figure below shows pressure variation in two different sound waves in air with time at a given position. Both the figures are drawn to the same scale.



Which of the following statement is true?

A simple wave motion is represented by $y=5\left(\sin 4\pi t+\sqrt{3}\cos 4\pi t\right)$. Its amplitude is

Two simple harmonic motion, are represented by the equations $y_1=10\sin \left(3\pi t+\frac{\pi }{3}\right); y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)$. Ratio of amplitude of $y_1$ to $y_2=x:1$. The value of $x$ is