The intensity of a wave is
(a) Proportional to square of the frequency
(b) Proportional to the velocity of wave
(c) Proportional to the density of the medium
(d) Proportional to the square of the distance of the source from the observer

Options

A. only d is true
B. a & b are true
C. a,b, & c are true
D. a,b,c & d are true

Answer

To solve the question regarding the intensity of a wave and its relationship with various factors, we will analyze each option step by step.

### Step 1: Understanding Intensity of a Wave
The intensity (I) of a wave is defined as the power per unit area carried by the wave. It can be mathematically expressed in terms of various parameters such as frequency, amplitude, density of the medium, and velocity of the wave.

### Step 2: Analyzing Each Option
1. **Option (a): Proportional to square of the frequency**
- The formula for intensity can be expressed as:
\[ I \propto A^2 \cdot \nu^2 \]
where \( A \) is the amplitude and \( \nu \) (nu) is the frequency. This shows that intensity is indeed proportional to the square of the frequency.
- **Conclusion**: This statement is **True**.

2. **Option (b): Proportional to the velocity of the wave**
- The intensity can also be expressed in terms of the wave's velocity (V):
\[ I \propto V \]
This indicates that intensity is directly proportional to the velocity of the wave.
- **Conclusion**: This statement is **True**.

3. **Option (c): Proportional to the density of the medium**
- The intensity of a wave is also influenced by the density of the medium (ρ):
\[ I \propto \rho \]
This shows that intensity is directly proportional to the density of the medium.
- **Conclusion**: This statement is **True**.

4. **Option (d): Proportional to the square of the distance of the source from the observer**
- The intensity of a wave decreases with the square of the distance from the source, following the inverse square law:
\[ I \propto \frac{1}{r^2} \]
This means intensity is inversely proportional to the square of the distance, not directly proportional.
- **Conclusion**: This statement is **False**.

### Final Conclusion
Based on the analysis:
- Options (a), (b), and (c) are **True**.
- Option (d) is **False**.

Thus, the correct answer is that options (a), (b), and (c) are true, making the answer option **3**.