Question

A stationary wave is formed in a well having
ten segments from the water surface to the top
of the well. If the wave length of wave is 1
meter, the depth of the well is
1) 4.25 m 2) 5.25 m 3) 3.25 m 4) 5m​

Answer 1

Answer: Length of each segment is lambda/4 = 0.25 m

There are ten segments so depth of well is 10 * 0.25 = 2.5m

Answer 2

The phenomenon is the result of interference; that is, when waves are superimposed, their energies either add or cancel. In the case of waves moving in the same direction, the interference creates a traveling wave. For oppositely moving waves, interference creates an oscillating wave fixed in space.

A vibrating rope tied at one end will produce a standing wave as shown in the figure; the train of waves (line B) bounces back after reaching the fixed end of the rope and superimposes itself as another train of waves (line C) in the same plane. Because of the interference between the two waves, the resulting amplitude (R) of the two waves will be the sum of their individual amplitudes. Part I of the figure shows that the B and C waveforms coincide so that the R standing wave has double the amplitude. In part II, 1/8 of a period later, B and C are each shifted by 1/8 of a wavelength. Part III presents the case 1/8 period even later when the amplitudes of the B and C component waves are oppositely directed. At all times there are positions (N) along the rope, called nodes, at which no movement occurs; there are two trains of waves always in opposition. On either side of the node is a vibrating antinode (A). The antinodes alternate in the direction of displacement, so that the rope at any moment resembles the graph of a mathematical function called a sine, as shown by line R. Both longitudinal (e.g. sound) waves and transverse (e.g. water) waves can be formed. standing waves.

The length of each segment is λ/4 = 0.25 m

There are ten segments so the depth of the well is 10 * 0.25 = 2.5m

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