Harmonic Motion and Waves

Oscillators An oscillator is a system with motion that repeats in cycles.

Period A full cycle is one complete back and forth motion. The period is the time it takes to complete one full cycle. Period T is measured in seconds.

Frequency Frequency is how many cycles are completed each second. Frequency f is measured in hertz, or Hz. 100 – 800 Hz

Frequency and period The period of an oscillator is one over its frequency. The frequency of an oscillator is one over its period.

What causes oscillations? Oscillations occur in systems with stable equilibrium. Stable systems have restoring forces that act to return them to the equilibrium position if they are displaced.

So, what is a wave? Drop a pebble on a pond on a calm day. As the pebble breaks the surface, the water oscillates up and down—in harmonic motion. Ripples form and spread out. An oscillation that travels is a wave.

Waves and energy Waves are an essential way in which energy travels from one place to another. Waves propagate through space, spreading energy out to other regions which may be quite far away.

Amplitude The amplitude A of a wave is the maximum amount the water rises or falls compared to its average resting level. The amplitude of different types of waves may have different units: A Water wave amplitude is a distance, in meters. Sound wave amplitude is a pressure, in pascals.

Wavelength λ The wavelength λ is the distance a wave travels before it begins to repeat itself. The distance of one cycle. The wavelength can be measured from peak to peak, or trough to trough. How many wavelengths appear in this figure?

Period Period is the time to complete one cycle or one wavelength. T = 9 seconds

Frequency The frequency f of a wave is a measure of how quickly it oscillates. The unit for frequency is the hertz, or Hz. One hertz equals one cycle per second.

Frequency The frequency of a wave conveys information. Frequency remains the same even if the wave amplitude decreases as it spreads out. the frequency of a light wave determines its color. the frequency of a sound wave determines its pitch.

Wave speed The speed of a wave depends on the type of wave and on its medium. Examples: speed of typical water waves: 5 m/s speed of sound in air: 343 m/s speed of light: 300,000,000 m/s (in a vacuum)

Wave speed As a wave moves forward, it advances one wavelength with each complete cycle. distance: speed: frequency: wave speed:

Energy and frequency The energy of a wave increases with frequency: lower energy higher energy low frequency high frequency (slower oscillations) (faster oscillations) long wavelength short wavelength

Energy and amplitude The energy of a wave also increases with amplitude: lower energy higher energy small amplitude large amplitude

Energy and amplitude As a wave spreads out, its amplitude decreases. One reason is damping; friction reduces the wave’s energy over time. Another reason is that as the wave propagates outward, its energy is spread over a larger area.