Ncert Exercises & Solutions

The following statements are given for a stationary wave:

a. Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.

b. All the particles cross their mean position at the same time.

c. All the particles are oscillating with the same amplitude.

d. There is no net transfer of energy across any plane.

e. There are some particles that are always at rest.

Choose the correct alternatives:

1. (a, b, d, e)

2. (a, c, d, e)

3. (b, c, d)

4. (c, d, e)

(1) Hint: Use the concept of standing waves.

Step 1: Find the time when the particles pass through the mean position.

Consider the equation of a stationary wave,

y = asin (kx) cosωt

Clearly, every particle at x will have amplitude

= asin kx =

fixed

For mean position, y=0

\Rightarrow cosωt = 0

\Rightarrow ωt = (2 n - 1) \frac{π}{2}

Hence, for a fixed value of n, all particles are having the same value of

time t = (2 n - 1) \frac{π}{2 ω}

[∵ ω = constant]

Step 2: Find the amplitude of the particles.

The amplitude of all the particles is a

\sin (kx)

which is different for different particles at different values of x

The energy of a stationary wave is confined between two nodes.

The particles at different nodes are always at rest.