(A) : Relative to an observer at rest in a medium the speed of a mechanical wave in that medium (1) depends only on elastic and other properties (such as mass density) of the medium. It does not depend on the velocity of the source.
(B): For an observer moving with velocity `v_(0)` relative to the medium, the speed of a wave is obviously different from v and is given by `v+-v_(0)`

Options

A. Both A and B are true
B. Both A and B are false
C. A is true, B is false
D. A is false, B is true

Answer

To solve the question, we will analyze both statements (A) and (B) regarding the speed of mechanical waves in a medium.

### Step-by-Step Solution:

**Step 1: Analyze Statement (A)**
Statement (A) claims that the speed of a mechanical wave in a medium depends only on the elastic properties and mass density of that medium and does not depend on the velocity of the source.

- **Explanation**: The speed of mechanical waves (like sound waves) in a medium is determined by the medium's properties, such as its elasticity (stiffness) and density. This means that regardless of how fast the source of the wave is moving, the speed of the wave in the medium remains constant as long as the properties of the medium do not change.

- **Conclusion**: Statement (A) is **True**.

**Step 2: Analyze Statement (B)**
Statement (B) states that for an observer moving with velocity \( v_0 \) relative to the medium, the speed of the wave is given by \( v \pm v_0 \).

- **Explanation**: When an observer is moving relative to the medium, the observed speed of the wave can change. If the observer moves in the same direction as the wave, the speed is \( v - v_0 \) (the wave speed minus the observer's speed). If the observer moves against the direction of the wave, the speed is \( v + v_0 \) (the wave speed plus the observer's speed).

- **Conclusion**: However, it is important to note that the speed of the wave itself (in the medium) remains independent of the observer's motion. The statement implies a change in the observed speed due to the observer's motion, which is correct. Therefore, Statement (B) is **True**.

### Final Conclusion:
- Statement (A) is **True**.
- Statement (B) is **True**.