PHYC10003 Chap.7 Travelling Waves
Travelling Waves
Travelling waves carry energy while particles remain near equilibrium. Their displacement depends on both position and time, unlike a single stationary oscillator. This chapter distinguishes transverse and longitudinal motion, decodes amplitude, wave number and angular frequency, uses constant phase to find direction, and explains why source frequency stays fixed while medium-dependent speed changes wavelength.
A travelling disturbance carries energy while individual medium particles oscillate around their own positions. Transverse motion is perpendicular to propagation, whereas longitudinal motion is parallel. In a sinusoidal equation, amplitude sets maximum displacement, wave number sets spatial phase rate, and angular frequency sets temporal phase rate. Their ratio gives phase speed.
Holding phase constant while time increases determines propagation direction without relying on an isolated sign rule. A spatial snapshot fixes time; a particle history fixes position. Their similar shapes do not make their horizontal axes interchangeable. Particle velocity comes from a time derivative at fixed position and is distinct from the speed of the pattern. At a boundary, the continuing source fixes frequency.
The new medium fixes speed, so wavelength adjusts through the speed-frequency relationship. For a stretched string, speed grows with the square root of tension and falls with the square root of linear density. Dimensional analysis, fixed-frequency reasoning, and direct phase tracking provide independent checks and prevent changes in medium from being assigned incorrectly to the source.
What this chapter covers
- 01
Energy transport without matter transport
- 02
Transverse and longitudinal waves
- 03
Frequency, wavelength and speed
- 04
Travelling-wave phase
- 05
Spatial snapshots and time histories
- 06
String speed from tension and linear density
Worked example · free
Decode a sinusoidal travelling wave
- 1Read amplitude as 0.040 m.
- 1Use wave number 5.0 to find wavelength 1.257 m.
- 1Use angular frequency 20 to find frequency 3.183 Hz.
- 1Divide angular frequency by wave number to get 4.0 m/s.
- 1The minus time term gives motion toward positive x.
Key terms
- Transverse Wave
- A transverse wave has particle displacement perpendicular to propagation.
- Longitudinal Wave
- A longitudinal wave has particle displacement parallel to propagation.
- Phase Speed
- Phase speed is the propagation speed of a point of constant phase such as a crest.
- Spatial Snapshot
- A spatial snapshot plots displacement against position at one fixed time.
- Linear Density
- Linear density is mass per unit length of a string or similar medium.
Travelling Waves FAQ
What stays fixed when a wave enters another medium?
The source frequency stays fixed because the boundary continues oscillating at the same rate. The new medium changes wave speed, so wavelength adjusts to keep speed equal to frequency times wavelength. Amplitude needs separate boundary information and cannot be inferred from the speed relation alone.
How do I tell wave direction from an equation?
Hold the phase constant and increase time. If x must increase to keep phase fixed, the wave travels toward positive x; if x must decrease, it travels toward negative x.
Why is particle speed different from wave speed?
Wave speed describes propagation of the disturbance pattern. Particle speed describes local medium motion and comes from the time derivative of displacement at a fixed position. They refer to different motions.
Exam move
Create a decoding table with amplitude, wave number, angular frequency, wavelength, frequency, phase speed, and direction. Fill it from several equations whose coefficients and signs vary, retaining radians and units. Determine propagation direction by holding phase constant and asking how position must change as time increases instead of relying on an isolated sign mnemonic.
Practise both spatial snapshots and particle histories by explicitly fixing one variable and labelling the horizontal axis. Translate a crest location forward by a short time to verify direction. Differentiate with respect to time at fixed position for particle velocity, then compare that local motion with the speed of a constant phase point. Name particle speed and phase speed in every answer so their meanings cannot merge.
For medium-boundary questions, write source frequency unchanged first, obtain the new speed from the medium rule or supplied data, and then recalculate wavelength. Predict the direction of the wavelength change before using numbers. For strings, reduce tension divided by linear density to speed-squared units and compare the square-root response to changes in tension or density.
Build ratio problems where tension is multiplied by four or linear density by nine so the square-root scaling is visible. Sketch transverse and longitudinal cases and mark particle motion relative to propagation. Explain how neighbouring particles pass energy onward without travelling with the pattern over the full distance.
Finish with a three-part check: the source controls frequency, the medium controls phase speed, and their quotient determines wavelength. Any answer that changes all three independently needs its causal assumptions revisited.
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