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Grade 10-11 (age 15-17)

high school physics Properties of Waves

Throw a stone into a lake and ripples spread out, but the water itself does not flow away; it bobs up and down in place, and only the disturbance and its energy move outward. A vibration spreading like this is a wave. If the vibration is perpendicular to the direction of travel the wave is transverse, and if it is parallel the wave is longitudinal; the wave speed v is the product of frequency f and wavelength λ, v = fλ. In a given medium the speed is fixed, so raising the frequency shortens the wavelength by the same factor. When two waves overlap their displacements add, and depending on the phase difference they reinforce each other (constructive interference) or cancel (destructive interference).

What a Wave Is

🌊 What Ripples Carry
①Throw a stone into a lake and ripples spread out in circles
②A leaf floating on the water only bobs up and down in place; it does not travel with the ripples
③A wave is a vibration passed from one place to the next, carrying energy as it goes
④The medium only vibrates in place; what travels far is the vibration and its energy

Classification

Transverse and Longitudinal Waves
ItemTransverseLongitudinal
Direction of vibrationPerpendicular to travelParallel to travel
ExamplesLight (electromagnetic waves), waves on a string, seismic S wavesSound, a spring pushed back and forth, seismic P waves
MediumWaves on a string need one; light does notNeeded (sound cannot travel through a vacuum)
FeaturesCan be polarizedAlternating compressions and rarefactions

Transverse Waves and v = fλ

5 Hz
5 (relative)
Wave Speed
v = fλ
Wave speed (m/s) = frequency (Hz) × wavelength (m)
💡 Why v = fλ
①If the source vibrates f times in 1 s, f waves are made in that time
②Each wave is λ long, so the distance the wave travels in 1 s is f × λ, which is the speed v
③The speed depends on the medium, so changing the frequency in the picture leaves v = 100 m/s unchanged and changes the wavelength to λ = v/f
④The amplitude A is a relative scale on screen. A larger A means the wave carries more energy (for sound, it is louder), but the speed and wavelength stay the same

Superposition and Interference

0°
Period and Frequency
T = 1f
The period (s) is the time for one vibration, the reciprocal of the frequency (Hz)
🔑 The Principle of Superposition
①Where two waves meet, the displacement is the sum of the two displacements (principle of superposition)
②With a phase difference of 0°, crest meets crest and the amplitude doubles (constructive interference)
③With a phase difference of 180°, crest meets trough and the amplitude becomes 0 (destructive interference)
④At a phase difference φ in between, the resultant's amplitude is 2|cos(φ/2)| times that of one wave
⑤After passing through each other, the two waves continue on their way with their original shapes

Four Properties of Waves

🔄 Reflection, Refraction, Interference, Diffraction
①Reflection: a wave bounces back at a boundary, with the angle of incidence equal to the angle of reflection
②Refraction: entering a new medium changes the speed and bends the direction of travel
③Interference: two overlapping waves reinforce or cancel each other
④Diffraction: a wave bends around an obstacle or through a narrow gap, and the longer the wavelength, the more it bends
⑤All four are shared by every kind of wave, including light, sound and water waves

Worked Examples

Example 1
What is the speed of a wave with frequency 50 Hz and wavelength 4 m?
1
Use the wave speed formula v = fλ.
v = fλ
2
Substitute f = 50 Hz and λ = 4 m.
v = 50 × 4 = 200 m/s
▸ 200 m/s
In 1 s, 50 waves are made and each is 4 m long, so the wave moves forward 200 m in 1 s.
Example 2
A sound wave travels at 340 m/s with a period of 0.002 s. What is its wavelength?
1
First find the frequency as the reciprocal of the period: f = 1/T.
f = 1T = 10.002 = 500 Hz
2
From v = fλ, compute λ = v/f.
λ = vf = 340500 = 0.68 m
▸ 0.68 m
When the period T is given, find the frequency first from f = 1/T, then use v = fλ.

Summary

The Key Wave Formula
v = fλ = λ/T
Speed = frequency × wavelength = wavelength ÷ period
CSAT-style problem, adapted
If the frequency of a wave in the same medium is doubled, how does the wavelength change?
①Doubles
②Quadruples
③Stays the same
④Halves
⑤Becomes one quarter
▸ ④ Halves
1
In the same medium the speed v is constant, so in v = fλ the frequency f and wavelength λ are inversely proportional.
v = fλ = constant
2
If f becomes 2 times larger, λ becomes half.
λ = vf ⇒ f×2 ⇒ λ÷2
🎯 Exam Points
①v = fλ is the basic relation linking wave speed, frequency and wavelength
②Wave speed depends on the medium and has nothing to do with frequency or amplitude
③In a transverse wave the vibration is perpendicular to travel (light); in a longitudinal wave it is parallel (sound)
④By the principle of superposition, the resultant displacement is the sum of the individual displacements
⑤Reflection, refraction, interference and diffraction are shared by all waves
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