What is a harmonic wave function ?

Answer

### Step-by-Step Solution:

1. **Definition of Harmonic Wave Function**:
A harmonic wave function is defined as a wave function that is periodic in nature. This means that it repeats itself at regular intervals.

2. **Characteristics of Harmonic Waves**:
- The wave function must be expressed in terms of sine or cosine functions. These trigonometric functions are inherently periodic.
- The general form of a harmonic wave can be written as:
\[ y(x, t) = A \sin(\omega t + \phi) \quad \text{or} \quad y(x, t) = A \cos(\omega t + \phi) \]
where:
- \( A \) is the amplitude of the wave,
- \( \omega \) is the angular frequency,
- \( t \) is time,
- \( \phi \) is the phase constant.

3. **Understanding Periodicity**:
- Both sine and cosine functions have a characteristic periodicity, meaning they repeat their values in regular intervals. This is what makes them suitable for describing harmonic waves.

4. **Conclusion**:
Therefore, a harmonic wave function is a periodic wave that can be mathematically represented using sine or cosine functions, which encapsulates the essential characteristics of wave motion.