If the energy density and velocity of a wave are u and c respectively then the energy propagating per second per unit area will be -

Options

A. uc
B. ` (c )/(u)`
C. `(u)/(c ) `
D. `c^(2)u`

Answer

To solve the problem, we need to find the energy propagating per second per unit area given the energy density (u) and the velocity of the wave (c).

### Step-by-Step Solution:

1. **Understanding Energy Density**:
Energy density (u) is defined as the energy (E) per unit volume (V) of the medium. Mathematically, this is represented as:
\[ u = \frac{E}{V} \]

2. **Relating Volume to Area and Length**:
The volume (V) can be expressed in terms of area (A) and length (L) as:
\[ V = A \cdot L \]
Thus, we can rewrite the energy density equation as:
\[ u = \frac{E}{A \cdot L} \]

3. **Understanding Wave Propagation**:
The velocity (c) of the wave is defined as the distance (L) traveled by the wave in a given time (T):
\[ c = \frac{L}{T} \]
This can be rearranged to express length in terms of velocity and time:
\[ L = c \cdot T \]

4. **Substituting Length in the Energy Density Equation**:
Now, substituting \(L = c \cdot T\) into the energy density equation:
\[ u = \frac{E}{A \cdot (c \cdot T)} \]
Rearranging this gives:
\[ E = u \cdot A \cdot (c \cdot T) \]

5. **Finding Energy Propagating per Second per Unit Area**:
To find the energy propagating per second per unit area, we need to divide the energy (E) by the product of area (A) and time (T):
\[ \frac{E}{A \cdot T} = u \cdot c \]

6. **Final Expression**:
Thus, the energy propagating per second per unit area is given by:
\[ \text{Energy propagating per second per unit area} = u \cdot c \]

### Final Answer:
The energy propagating per second per unit area is \( u \cdot c \).