At a certain instant, a stationary transverse wave is found to have maximum kinetic energy. The appearance of string at that instant is

Options

A. sinusoidal shape with amplitude A/3
B. sinusoidal with amplitude A/2
C. sinusoidal shape with amplitude A
D. straight line

Answer

To solve the problem, we need to analyze the behavior of a stationary transverse wave and its kinetic energy at a specific instant. Here's a step-by-step breakdown:

### Step 1: Understand the nature of stationary transverse waves
A stationary transverse wave is formed by the superposition of two waves traveling in opposite directions. In such a wave, certain points (nodes) remain stationary, while others (antinodes) oscillate with maximum amplitude.

**Hint:** Recall that in a stationary wave, particles oscillate about their mean position.

### Step 2: Identify the condition for maximum kinetic energy
In simple harmonic motion (SHM), the kinetic energy of a particle is maximum when it is at its mean position (the equilibrium position). This is because, at this point, the particle has the highest velocity.

**Hint:** Remember that kinetic energy is related to the velocity of the particles in SHM.

### Step 3: Relate the kinetic energy condition to the wave
For the entire string to have maximum kinetic energy at a certain instant, all particles of the string must be at their mean positions simultaneously. This means that the wave must not have any displacement from the mean position at that instant.

**Hint:** Think about what the shape of the wave would look like if all points are at their mean position.

### Step 4: Determine the appearance of the string
If all particles of the string are at their mean positions, the wave will appear as a straight line. This is because there will be no oscillation or displacement from the equilibrium position at that instant.

**Hint:** Visualize the wave: if every point is at the mean position, how would the wave look?

### Step 5: Conclusion
Given that all particles are at their mean position, the appearance of the string at that instant will be a straight line.

**Final Answer:** The appearance of the string at that instant is a straight line.