1. What are progressive waves? Describe briefly the properties of longitudinal progressive waves.
2. Derive the relation
d2y/dt2 = V 2 d2y dx2
3. Distinguish between particle velocity and wave velocity and obtain the relation between the two.
4. Show that for a plane progressive wave, on the average, half the energy is kinetic and half potential. Hence derive the expression for intensity of sound in terms of pressure amplitude.
5. Show that u = – v dy/dx , , where u is the particle velocity and v is the wave velocity.
6. Show that the energy of a plane progressive wave is given by
E = 2π2 pn2 a2
7. Derive the equation of wave motion in the form of
y = a sin 2π /λ (vt- x)
8. Deduce the equation of simple harmonic wave travelling in the positive x direction in the form of y 2n = a sin2π /λ (vt – x) and explain how energy is distributed in such a progressive wave.
9. Differentiate between
(a) wave velocity and particle velocity
(b) progressive and stationary waves.
10. What are nodes and antinodes? Calculate the average kinetic and potential energy for a plane