Unit 10 ยท Lesson 1

๐ŸŒŠWave Properties

What is a Wave?

A wave is a disturbance that carries energy through a medium (or through empty space) without carrying matter along with it.

Types of waves: - Transverse waves: particles vibrate perpendicular to the direction of wave travel (light, string waves) - Longitudinal waves: particles vibrate parallel to the direction of wave travel (sound waves)

Key wave properties: - Amplitude (A): maximum displacement from equilibrium. Determines the energy/intensity of the wave. - Wavelength (ฮป): distance between two consecutive identical points (crest-to-crest or trough-to-trough). Measured in meters. - Period (T): time for one complete oscillation (s) - Frequency (f): number of oscillations per second (Hz = 1/s)

Wave Superposition

When two waves meet, they superpose (add together):

- Constructive interference: waves in phase โ†’ amplitudes add โ†’ bigger wave - Destructive interference: waves out of phase โ†’ amplitudes subtract โ†’ smaller (or zero) wave

After passing through each other, waves continue unchanged โ€” they don't permanently affect each other.

Wave Properties Visualization

See how amplitude and wavelength affect the wave shape. Two waves superposing shows interference.

๐Ÿ“ Key Equations

Wave properties

f = (1)/(T)
v = fฮป
E โˆ Aยฒ (energy proportional to amplitude squared)

โš ๏ธ Common Mistakes

โŒ

Misconception: Waves transport matter from one place to another.

โœ“ Correct thinking: Waves transport energy, not matter. The medium's particles oscillate in place and return to equilibrium.

Why: Think of a wave on a rope: the rope itself doesn't travel along; only the disturbance (energy) moves forward.

โŒ

Misconception: A larger amplitude means a higher frequency.

โœ“ Correct thinking: Amplitude and frequency are independent properties. Amplitude controls energy; frequency controls pitch (for sound) or colour (for light).

Why: You can have a loud low-pitched sound (large amplitude, low frequency) or a quiet high-pitched sound (small amplitude, high frequency).

โŒ

Misconception: Destructive interference destroys the energy of both waves.

โœ“ Correct thinking: Destructive interference cancels displacement locally, but the energy is redistributed โ€” not destroyed.

Why: Energy is conserved. Where waves cancel (nodes), the energy appears elsewhere as kinetic energy or at antinodes.

๐Ÿ“ Practice Problems

Try these problems. Check your answer when ready.

#1

A wave has a period of 0.02 s. What is its frequency?

easy
f = 1/T
#2

A wave has a frequency of 200 Hz and a wavelength of 1.7 m. What is its speed?

easy
#3

Wave A has amplitude 3 cm and wave B has amplitude 6 cm. How do their energies compare?

medium
E โˆ Aยฒ
#4

Two identical waves with amplitude 5 cm superpose in phase. What is the amplitude of the resulting wave? If they superpose exactly out of phase?

medium
#5

A transverse wave on a rope has wavelength 0.4 m and period 0.1 s. What is the wave speed? If the amplitude is doubled, how does the speed change?

hard

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