Waves Notes

Waves Unit – Packet 6.2

Driving Question: What determines the properties of waves?
Difference between longitudinal and transverse waves.
Periodic wave determinants: wavelength & amplitude.
Standing wave patterns affect music from stringed instruments.

Wave Movement

Waves transfer energy without physical movement of matter.
Waves can cause displacement, not change location.

Slinky Example

Energy moves through a stretched Slinky when one end is moved back and forth.
Parts of the Slinky stretch or compress, but the whole stays in its original position.
A compressed or displaced region moves from one end to the other, known as the pulse.
The speed of a pulse is determined by tension and mass.

Types of Waves

Longitudinal: movement in a substance matches the direction of the wave's travel (e.g., sound waves).
Transverse: disturbance is perpendicular to the wave's direction (e.g., light).
Ocean waves are both longitudinal and transverse, causing circular motion.

Harmonic Waves

Height of a wave = amplitude.
Distance between pulses = wavelength (\lambda).
Time between pulses = period (T).
Frequency = 1/T.
Wave speed: v = \frac{\lambda}{T} = f\lambda
When a wave enters a new medium, speed and wavelength change, but frequency remains constant.
If v increases, then \lambda increases. If v decreases, then \lambda decreases.

Interference

When a pulse reaches the end and bounces back, interference occurs.
Principle of Superposition: total disturbance equals the sum of each individual disturbance.
Constructive interference: waves are in phase, creating a larger combined wave.
Destructive interference: waves are out of phase, causing a cancellation effect.

Standing Wave Patterns

Nodes: Points in the wave pattern that are not displaced.
Antinodes: Points in the wave pattern that are displaced the most.

Stringed Instruments

Create music using standing waves on their strings.
Frequency matches string vibration frequency, determining musical pitch.
Longer string length (L) creates a lower frequency.

Harmonics

Fundamental (first harmonic): Simplest standing wave with nodes at both ends and an antinode in the middle; \lambda = 2L.
Frequency: f = \frac{v}{\lambda} = \frac{v}{2L}
Second harmonic: Node at the midpoint; \lambda = L; frequency is twice the fundamental.
Third harmonic: Four nodes and three antinodes; frequency is three times the fundamental.

Octaves

Intervals where the higher note has twice the frequency of the lower one.
If the fundamental frequency is 100 Hz, the next octave would be at 200 Hz, then 400 Hz, and so on.