The dimensions of intensity of wave are

Options

A. `[M L^(2) T^(-3)]`
B. `[M L^(0) T^(-3)]`
C. `[M L^(-2) T^(-3)]`
D. `[M^(1) L^(2) T^(3)]`

Explanation

To find the dimensions of intensity of a wave, we can follow these steps:

### Step 1: Understand the Definition of Intensity
Intensity (I) is defined as power (P) per unit area (A). Mathematically, it can be expressed as:
\[ I = \frac{P}{A} \]

### Step 2: Determine the Dimensions of Power
Power is defined as the rate of doing work or the rate of energy transfer. The dimensions of energy (E) are given by:
\[ [E] = [M][L^2][T^{-2}] \]
where:
- \( M \) is mass,
- \( L \) is length,
- \( T \) is time.

Since power is energy per unit time, we have:
\[ [P] = \frac{[E]}{[T]} = \frac{[M][L^2][T^{-2}]}{[T]} = [M][L^2][T^{-3}] \]

### Step 3: Determine the Dimensions of Area
Area (A) is given by the square of length:
\[ [A] = [L^2] \]

### Step 4: Combine Dimensions to Find Intensity
Substituting the dimensions of power and area into the intensity formula:
\[ [I] = \frac{[P]}{[A]} = \frac{[M][L^2][T^{-3}]}{[L^2]} \]

### Step 5: Simplify the Expression
When we simplify the expression:
\[ [I] = [M][L^2][T^{-3}] \cdot [L^{-2}] = [M][L^0][T^{-3}] = [M][T^{-3}] \]

### Conclusion
Thus, the dimensions of intensity of a wave are:
\[ [I] = [M][T^{-3}] \]

### Final Answer
The dimensions of intensity of wave are \( [M][T^{-3}] \).

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