Progressive waves flashcards

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Progressive wave
A disturbance that travels through a medium (or space), transferring energy without a net transfer of the medium.
Displacement (of a particle in a wave)
Distance and direction of the particle from its equilibrium position.
Amplitude
The maximum displacement of a particle from its equilibrium position. Half the crest-to-trough height.
Wavelength
The distance between two neighbouring points oscillating in phase, e.g. crest to crest or compression to compression.
Period
The time for one complete oscillation of a particle (s).
Frequency
The number of complete oscillations per unit time; unit hertz, 1 Hz = 1 s⁻¹.
Wave speed
The distance travelled by the wave (e.g. by a crest) per unit time.
Transverse wave
Oscillations perpendicular to the direction of energy transfer. E.g. all EM waves, waves on strings.
Longitudinal wave
Oscillations parallel to the direction of energy transfer. E.g. sound, ultrasound, P-waves.
Compression
Region of a longitudinal wave where particles are closest together; pressure and density above normal.
Rarefaction
Region of a longitudinal wave where particles are furthest apart; pressure and density below normal.
Phase difference
How far one oscillation is ahead of another, as a fraction of a cycle, in degrees or radians (one cycle = 360° = 2π rad).
The wave equation
v = fλ (Yes)
Frequency and period
f = 1/T (No — learn it)
Wave speed from the two graphs
v = λ/T (λ from the displacement–distance graph, T from the displacement–time graph). (No — derive it)
Phase difference between points Δx apart
Δφ = 360° × Δx/λ = 2πΔx/λ (No — learn it)
Displacement–distance graph: what is the repeat length?
The wavelength λ. The graph is a snapshot of the whole wave at one instant.
Displacement–time graph: what is the repeat length?
The period T. The graph follows one particle over time.
Longitudinal wave on a displacement–distance graph: where is a compression?
At a zero of displacement where molecules on both sides are displaced towards it (displacement going from + to − in the direction of travel).
Where is the pressure greatest in a sound wave, compared with the displacement graph?
At compressions, where the displacement is zero; pressure variation is λ/4 out of step with displacement.
Snapshot taken a quarter of a period later
Same shape, shifted λ/4 in the direction of travel.
Why is v = fλ true?
In one period T the wave moves forward one wavelength λ, so v = λ/T = fλ.
A wave enters a new medium: what changes?
Frequency stays the same (set by the source); speed and wavelength change in the same ratio.
Points in phase and in antiphase along a wave
In phase: λ, 2λ, 3λ … apart. Antiphase (180°, π rad): λ/2, 3λ/2 … apart.
How does sound travel from a loudspeaker to your ear?
The cone pushes air into compressions and pulls it into rarefactions; molecules oscillate about fixed positions, passing energy on; pressure at the ear varies at the source frequency.
Speed of sound practical: what is connected to each oscilloscope channel?
Channel 1: signal generator (which also drives the loudspeaker). Channel 2: microphone.
Speed of sound practical: how is λ found?
Move the microphone away from the loudspeaker; the traces return to being in phase once per wavelength moved. λ = distance ÷ number of wavelengths.
Speed of sound practical: why measure over many wavelengths?
The uncertainty in locating each in-phase position is fixed, so it becomes a smaller percentage of a longer distance.
Sound of frequency 686 Hz in air at 343 m s⁻¹. Wavelength?
λ = v/f = 343 ÷ 686 = 0.500 m.
Microwaves of frequency 2.45 GHz. Wavelength?
λ = c/f = 3.00 × 10⁸ ÷ 2.45 × 10⁹ = 0.122 m.
A displacement–time graph repeats every 2.5 ms. Frequency?
f = 1/T = 1 ÷ 2.5 × 10⁻³ = 400 Hz.
Two points 0.15 m apart on a wave of wavelength 0.60 m. Phase difference?
360° × 0.15 ÷ 0.60 = 90° (π/2 rad).
Ten ripple crests in a row span 0.36 m; the dipper vibrates at 15 Hz. Wave speed?
Ten crests = nine gaps: λ = 0.36 ÷ 9 = 0.040 m; v = 15 × 0.040 = 0.60 m s⁻¹.
Speed of sound practical at 3.00 kHz: microphone moved 0.684 m through six wavelengths. Speed?
λ = 0.684 ÷ 6 = 0.114 m; v = 3000 × 0.114 = 342 m s⁻¹.
n crests in a row span how many wavelengths?
n − 1. Count the gaps, not the crests.
Amplitude from crest-to-trough height
Halve it. Crest to trough is 2A.
Defining transverse/longitudinal: what must you mention?
What oscillates, and its direction compared with the direction of energy transfer (perpendicular / parallel).
Before reading a wave graph
Check the horizontal axis: distance gives λ, time gives T.

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