Final answer:
Mechanical waves can indeed be periodic, characterized by a pattern that repeats at regular intervals. The frequency of a wave is the inverse of its period, and simple harmonic motion is a case of periodic motion that requires constant frequency which does not depend on amplitude.
Step-by-step explanation:
Can mechanical waves be periodic? Yes, mechanical waves can indeed be periodic waves. Periodicity in mechanical waves is characterized by a consistent pattern that repeats at regular intervals. The fundamental period of a wave is the time it takes for one complete cycle of the wave to pass a given point.
To determine if a discrete-time signal is periodic and to find its fundamental period, you would examine if there's a smallest non-zero value T for which the signal repeats itself, such that signal(t) = signal(t + T) for all time t.
When considering simple harmonic motion, this motion is only considered to be harmonic when the frequency is constant, which means it does not depend on the amplitude of oscillation; an example includes a mass-spring system oscillating without external forces acting on it.
However, there can be scenarios in more complex systems where the frequency may depend slightly on amplitude due to non-linear effects, but these would not be classified as simple harmonic motion.
Key Concepts for Understanding Periodicity in Waves:
- Relation between period and frequency: Frequency (f) is the inverse of the period (T), meaning f = 1/T.
- Simple Harmonic Motion: Requires constant frequency and is a special case of periodic motion.
- Ocean waves not being perfectly sinusoidal is an example of real-world phenomena where ideal models (like simple harmonic motion) are approximations.