Question

When a stone is dropped in to the river, certain waves are formed on its surface.

1. What type of wave it is?

2.  Is it a progressive wave? Explain.

3. If yes, derive a mathematical expression for the above wave.

Answer 1

1. Transverse wave.

2. Yes, because each particles of the medium vibrates simple harmonically.

3. Consider a harmonic wave travelling along the +ve x-direction with a speed V. Let ‘0’ be the particle in the medium. Its displacement at any instant of time may be written as y = A sin ωt

Consider another particle ‘p’ at a distance x from ‘0’ to its right. The displacement of p at any instant.

y = A sin (ωt – α) ______(1)

α is the phase difference between 0 and P. Here

α = \(\frac{2π}{λ}\)x equation (1) becomes