Transverse and Longitudinal waves

Which of the following transverse waves requires a medium for propagation.

The expression for a sinusoidal wave at a fixed location can be written as:

 In a region of constant potential

 What are gravitational waves?

Equipotential surface of a greater distance from a collection of charge whose total sum is not zero one approximately.

A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will.

What is the frequency of capillary(water) waves?

The electric field associated with an electromagnetic wave in vacuum is given by $\overrightarrow{E}=40 \cos \left(kz-6\times {10}^{8}t\right) \hat{i}$, where $E$, $z$ and $t$ are in volt per meter, meter and second respectively. The value of wave number $k$ is

The frequency of an electromagnetic wave is $6\times {10}^{15}\mathrm{ }{\mathrm{s}}^{-1}$ . Its wave number would be

The equation of a SHM is given by y=$10\sin \left(\frac{2\pi }{45}t+a\right)$. If the displacement is 5 cm at t=0, then the total phase at t=7.5s is

A wave function is $y=0.1 \sin [100\pi t-kx]$ and wave velocity is $100 \mathrm{m} {\mathrm{s}}^{-1}$, its wave number is equal to

The equation of a wave is given by $y=10\sin \left(\frac{2\pi }{45}t+a\right)$. If the displacement is $5 \mathrm{cm}$ at $t=0$, then the total phase at $t=7.5 \mathrm{s}$ is

A plane progressive wave is given by y=2cos 6.284 (30t-x). What is period of the wave?

The wave described by $y=0.25 \sin \left(10\pi x-2\pi t\right)$, where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along the

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

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

A metal wire of linear mass density of $9.8 \mathrm{g} {\mathrm{m}}^{-1}$ is stretched with a tension of $10 \mathrm{kg}-\mathrm{wt}$ between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $\upsilon$. The frequency $\upsilon$ of the alternating source is