Gravity Waves Formation Explained
This question asks about the necessary conditions for gravity waves to form in shallow water.
Understanding Gravity Waves
Gravity waves are waves where the restoring force is gravity. In fluids, they typically occur at the interface between two fluids of different densities or at the surface of a fluid exposed to another medium (like air).
For waves to form and propagate, there must be a mechanism for the fluid to be displaced and then restored to its equilibrium position by a force. In the context of gravity waves:
- Restoring Force: Gravity acts downwards on the displaced fluid.
- Displacement Mechanism: The fluid needs a surface or interface that can move vertically.
Analysing the Conditions
The question states that gravity waves in shallow water can form if the fluid has either:
- A specific type of surface.
- An internal density discontinuity.
Let's examine the options provided for the type of surface:
- Free Surface: This refers to a surface open to the atmosphere or another fluid, allowing for vertical displacement. Think of the surface of a lake or the ocean. This is a key requirement for surface gravity waves.
- Hard Surface: A hard, rigid surface prevents the fluid from moving vertically, thus inhibiting wave formation.
- Smooth Surface: While waves might appear smooth, "smooth" describes the texture or lack of disturbances, not the physical requirement of an interface capable of displacement. A smooth surface could still be rigid.
- Moderate Surface: This term is vague and doesn't describe a specific physical condition necessary for wave formation.
The formation of gravity waves relies on the presence of an interface that can deform. A free surface provides this essential interface, allowing gravity to act as the restoring force when the fluid is displaced. Similarly, an internal density discontinuity (like the boundary between different layers of water at different temperatures or salinities) acts as an interface where internal gravity waves can form.
Conclusion
Therefore, gravity waves in shallow water require a free surface or an internal density discontinuity to form. The term "free" accurately describes the necessary condition of an open, deformable interface.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
