STATEMENT-1 : Beats will be heard if a tuning fork is sounded along with a sonometer wire with the same fundamental frequency as the tuning fork
because
STATEMENT -2 : Beats are caused by alternate constructive and destructive interference between two sounds.

Options

A. Statement -1 is True, statement -2 is True, Statement -2 is a correct explanation for Statement -1.
B. Statement -1 is True, Statement -2 is True , Statement-2 is Not a correct explanation for statement-1
C. Statement -1 is True, statement -2 is False
D. Statement -1 is False, Statement -2 is True.

Answer

To analyze the statements provided in the question, we will break down the reasoning step by step.

### Step 1: Understanding Beats
Beats occur when two sound waves of slightly different frequencies interfere with each other. The phenomenon of beats is characterized by alternating periods of constructive interference (where the sound waves amplify each other) and destructive interference (where the sound waves cancel each other out).

**Hint:** Remember that beats are a result of the interference of two waves with different frequencies.

### Step 2: Analyzing Statement 1
The first statement claims that beats will be heard if a tuning fork is sounded along with a sonometer wire that has the same fundamental frequency as the tuning fork.

- If both the tuning fork and the sonometer wire produce sound waves of the same frequency, the difference in frequency (Δf) between the two sounds is zero (Δf = f1 - f2 = 0).
- According to the formula for beats, the number of beats per second (x) is given by x = Δf. Therefore, if Δf = 0, then x = 0, meaning no beats will be heard.

**Hint:** Consider what happens when two frequencies are the same; how does this affect the beat frequency?

### Step 3: Analyzing Statement 2
The second statement explains that beats are caused by alternate constructive and destructive interference between two sounds.

- This statement is true because it accurately describes the phenomenon of beats. When two sound waves of slightly different frequencies interfere, they create a pattern of loud and soft sounds, which we perceive as beats.

**Hint:** Focus on the definition of beats and how they relate to sound wave interference.

### Conclusion
- **Statement 1** is **false** because no beats will be heard when the frequencies are the same (Δf = 0).
- **Statement 2** is **true** because it correctly describes the mechanism by which beats occur.

### Final Answer
- Statement 1: False
- Statement 2: True