Which of the following statements are true for wave motion ?

Options

A. Mechanical transverse waves can propagate through all mediums
B. Longitudinal waves can propagate through solids only.
C. Mechanical transverse waves can propagate through solids only.
D. Longitudinal waves can propagate through vacuum.

Explanation

To determine which statements are true for wave motion, let's analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** Mechanical transverse waves can propagate through all mediums.

**Analysis:** This statement is incorrect. Mechanical transverse waves require a medium with elasticity to propagate. Air does not have sufficient elasticity for transverse waves to form, as the particles cannot oscillate in a transverse manner (up and down) without returning to their original position. Therefore, this statement is false.

### Step 2: Analyze the second statement
**Statement:** Longitudinal waves can propagate through solids only.

**Analysis:** This statement is also incorrect. Longitudinal waves can propagate through solids, liquids, and gases. A common example is sound, which is a longitudinal wave that travels through air (gas) and water (liquid). Therefore, this statement is false.

### Step 3: Analyze the third statement
**Statement:** Mechanical transverse waves can propagate through solids only.

**Analysis:** This statement is correct. Mechanical transverse waves require a medium with elasticity, which is primarily found in solids. In solids, particles can oscillate perpendicular to the direction of wave propagation, allowing transverse waves to travel. Therefore, this statement is true.

### Step 4: Analyze the fourth statement
**Statement:** Longitudinal waves propagate through vacuum.

**Analysis:** This statement is incorrect. Longitudinal waves, such as sound waves, require a medium (solid, liquid, or gas) to propagate. They cannot travel through a vacuum because there are no particles to transmit the wave. Therefore, this statement is false.

### Summary of Findings
- Statement 1: False
- Statement 2: False
- Statement 3: True
- Statement 4: False

### Conclusion
Only the third statement is true: **Mechanical transverse waves can propagate through solids only.**

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