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Progressive Waves Exercise

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

progressive wave.