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13.2Vibrations and Waves

Wave Properties — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 4 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Distinguish transverse and longitudinal waves with examples.Wave speed = frequency × wavelengthv = fλ (m/s = Hz × m).Frequency and periodf = 1/T, so also v = λ/T.Speed = distance ÷ timev = d/t, useful for timing a pulse.Waves transfer energy, not matter; each particle only oscill…

  • Two kinds of graph are used
  • Amplitude is related to the energy carried
  • A water wave has frequency 2.5 Hz and wavelength 0.80 m. What is its speed?
  • Mechanical wave
  • Transverse wave
  • Wavelength (λ)

Section 1 of 7Wave Properties

Essential knowledge
13.2 Wave Properties concept map: Wave speed = frequency × wave, Frequency and period, Speed = distance ÷ time, Two kinds of graph are used, Amplitude is related to the e
Visual guide to the key ideas explained in this lesson.
A wave is a travelling disturbance that carries energy. The medium's particles oscillate about fixed positions; they do not travel with the wave. A cork on a pond bobs up and down but does not move along with the ripples.
Mechanical waves require a medium because the disturbance is passed between neighbouring particles. Electromagnetic waves are oscillating electric and magnetic fields and can travel through a vacuum.
In a transverse wave the vibration is at right angles to the direction the wave travels. Displacement–distance graphs show crests and troughs; the wavelength can be read as the distance between neighbouring crests.
In a longitudinal wave the vibration is along the direction of travel, producing compressions (high pressure) and rarefactions (low pressure). One wavelength is from the centre of one compression to the centre of the next.
Two kinds of graph are used
Two kinds of graph are used displacement–distance (a "snapshot"), from which you read wavelength and amplitude; and displacement–time (one point over time), from which you read period and amplitude. Don't confuse λ with T.
The wave equation v = fλ follows from speed = distance/time: in one period T the wave moves one wavelength λ, so v = λ/T = fλ.
The speed of a wave depends only on the medium (its properties such as tension, density, depth or stiffness). For a given medium, if frequency increases, wavelength decreases so that v stays constant.
When a wave crosses into a different medium, the frequency is unchanged (it is fixed by the source), but speed and wavelength change together.
Amplitude is related to the energy carried
Amplitude is related to the energy carried a larger amplitude wave carries more energy. For sound this is heard as loudness; for light it is brightness.
Wavefronts are lines of constant phase; rays drawn at right angles to wavefronts show the direction of travel of the wave.
Seismic P-waves are longitudinal and travel through solids and liquids; S-waves are transverse and travel only through solids – evidence for Earth's liquid outer core.

Section 2 of 7Process & sequence

1
Fill a ripple tank with shallow water to an even depth and switch on the lamp above to project wavefronts onto a screen below.
2
Switch on the vibrating bar (dipper) to produce straight (plane) wavefronts at a steady frequency.
3
Use a stroboscope or take a photo with a ruler in view to "freeze" the pattern.
4
Measure across 10 wavefronts and divide by 10 to find the wavelength λ.
5
Count waves passing a point in 10 s (or read the motor setting) and divide by 10 to find f.
6
Calculate v = fλ; repeat at another frequency to show speed stays the same in the same depth.

How a longitudinal wave travels along a slinkywrite these steps in this order; each step is a marking point.

1
Hand pushes the end coils forward, squeezing them into a compression.
2
The compressed coils push on the next coils, passing the compression along.
3
Hand pulls back, spreading coils into a rarefaction that follows the compression.
4
Repeating push–pull at frequency f sends a train of compressions and rarefactions.
5
Each coil only oscillates back and forth about its rest position while energy moves along.

Section 3 of 7Compare

Transverse vs longitudinal waves
PropertyTransverseLongitudinal
Direction of vibrationPerpendicular to energy transferParallel to energy transfer
FeaturesCrests and troughsCompressions and rarefactions
Wavelength measuredCrest to next crestCompression to next compression
ExamplesLight and all EM waves, ripples, string waves, S-wavesSound, ultrasound, P-waves, push on a slinky
Travel in vacuum?EM waves yes; mechanical transverse noNo (sound needs a medium)
What sets each wave quantity
QuantitySet byChanges on entering a new medium?
Frequency fThe sourceNo
Speed vThe mediumYes
Wavelength λBoth (λ = v/f)Yes, in proportion to v

Section 4 of 7Worked examples

Worked examples
A water wave has frequency 2.5 Hz and wavelength 0.80 m. What is its speed?
A water wave has frequency 2.5 Hz and wavelength 0.80 m. What is its speed?
  • v = fλ = 2.5 Hz × 0.80 m = 2.0 m/s.
    What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
3.06 m
A radio station broadcasts at 98.0 MHz. Radio waves travel at 3.00 × 108 m/s. Find the wavelength.
  • λ = v/f = 3.00 × 108 m/s ÷ 98.0 × 106 Hz = 3.06 m (3 s.f.).
0.45 m
A wave passes from deep water (v = 1.2 m/s, λ = 0.60 m) into shallow water where v = 0.90 m/s. Find the new wavelength.
  • f = v/λ = 1.2 ÷ 0.60 = 2.0 Hz (unchanged). New λ = v/f = 0.90 m/s ÷ 2.0 Hz = 0.45 m.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Wave · Mechanical wave · Transverse wave · Longitudinal wave · Wavelength (λ) · Crest and trough · Compression · Rarefaction · Amplitude · Frequency (f) · Wave speed (v) · Wavefront · Phase · Pulse
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
waves carry particles alongwaves transfer energy without transferring matter.
2
longitudinal waves vibrate in the same directionparticles vibrate parallel to the direction of energy transfer.
3
the frequency changes when the wave slows downthe frequency stays the same; speed and wavelength decrease.
4
wavelength is the length of the wavewavelength is the distance between two consecutive crests (or compressions).
5
amplitude is from crest to troughamplitude is from the rest position to a crest.

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