7. Waves

A wave is a travelling disturbance that transfers energy without requiring the medium’s particles to travel with the wave overall.

Describe what oscillates and the direction of energy transfer. Mechanical waves need a medium; electromagnetic waves do not.

A pulse along a rope moves down the rope while each small section moves mainly up and down around its equilibrium position.

The material itself is not carried from source to receiver at the wave speed; particle motion and wave propagation are different.

Amplitude is maximum displacement; period T is time per cycle; frequency f is cycles per second with f=1/T; phase difference compares positions in their cycles.

Use the same reference point when comparing phase. Amplitude is not the wavelength, and frequency is not the wave speed.

A 5 Hz oscillator has period 0.20 s; two points half a cycle apart differ in phase by 180°.

Points can be in phase even when separated by one wavelength, and larger amplitude does not automatically mean higher frequency.

On a cathode-ray oscilloscope, the time-base sets horizontal time per division and the y-gain sets vertical voltage per division.

Count divisions between peaks or from the baseline, then multiply by the relevant scale. Use a stable trigger before reading a period.

Four horizontal divisions at 2 ms div⁻¹ give a 8 ms period and frequency 125 Hz.

The vertical height measures voltage, not time; confusing the two scales produces plausible but wrong frequencies or amplitudes.

For a progressive wave, v=fλ, where v is speed, f frequency and λ wavelength. The relation follows because one wavelength travels in one period.

Use frequency in hertz and wavelength in metres. In a fixed medium, changing frequency generally changes wavelength so that the speed remains set by the medium.

A 250 Hz sound wave with wavelength 1.36 m travels at 340 m s⁻¹.

Frequency is set by the source, while speed is not automatically equal to frequency; do not confuse v with particle oscillation speed.

For a progressive wave, v=fλ: the wave speed equals frequency multiplied by wavelength.

If the medium fixes v, a change in source frequency changes wavelength inversely. Use metres and hertz so the result is m s⁻¹.

If a wave travels at 12 m s⁻¹ with frequency 4.0 Hz, its wavelength is 3.0 m.

The wave speed is not the same as the speed of individual particles oscillating in the medium.

A progressive wave carries energy from a source to new positions while the medium’s particles oscillate about equilibrium.

Track both the propagation direction and particle motion. Energy transfer does not require the material to move with the wave overall.

A ripple travels across water and can move a floating cork up and down while delivering energy to the edge.

A travelling wave is not a single object moving through the medium; phase and energy move through repeated oscillations.

Intensity I=P/A is power crossing unit area. For a wave in a fixed medium, I is proportional to amplitude squared: I∝A².

Keep the area definition separate from amplitude scaling. Doubling amplitude gives four times intensity, not twice.

If a speaker’s amplitude is reduced to one half under comparable conditions, the intensity becomes one quarter.

Intensity is not simply amplitude, and the inverse-square fall with distance is a separate geometric effect.

In a transverse wave, particles oscillate perpendicular to propagation; in a longitudinal wave, they oscillate parallel, producing compressions and rarefactions.

Classify the wave from particle motion, not from whether it is visible or mechanical. Polarisation is possible only for transverse waves.

A rope pulse is transverse; sound in air is longitudinal because air pressure changes travel through compressions.

Longitudinal does not mean “slow”, and transverse does not mean “up-down” in every orientation.

A displacement–distance graph shows the shape at one instant and a displacement–time graph shows one point’s oscillation; wavelength and period must be read from the correct axis.

Measure crest-to-crest or equivalent phase spacing for λ, and cycle time for T. Do not mix a spatial graph with a time graph.

A displacement–distance graph with 0.80 m between adjacent crests has λ=0.80 m; a time graph with 0.20 s per cycle has f=5 Hz.

Amplitude is read vertically on both graphs, but horizontal scale represents distance in one and time in the other.

When a sound source moves relative to an observer, wavefront spacing changes, so the observed frequency differs from the emitted frequency.

Approaching motion produces compressed wavefronts and higher observed frequency; receding motion produces greater spacing and lower frequency.

A passing siren sounds higher before it reaches you and lower after it passes, even though the siren emits a steady tone.

The Doppler shift is not caused by the source changing its intrinsic frequency; it is a relative-motion observation effect.

For a source moving relative to a stationary observer in a medium, f_o=f_s v/(v±v_s), using the sign that gives higher frequency for approach and lower for recession.

Define source speed and wave speed in the medium, then choose the sign from the physical motion rather than memorising it blindly.

An approaching siren produces compressed wavefronts, so f_o exceeds f_s; after passing, the denominator changes and the observed frequency falls.

The source speed is measured relative to the medium in this model, not automatically relative to the observer; the sign must match approach or recession.

Electromagnetic waves consist of mutually perpendicular electric and magnetic fields, both transverse to the direction of travel, and move at c≈3.00×10⁸ m s⁻¹ in vacuum.

They do not require a material medium; in matter their speed can be lower and depends on the medium.

Radio, visible light and X-rays are different frequencies of the same transverse electromagnetic family.

“Electromagnetic” does not mean longitudinal, and c applies to free space, not every material.

The principal regions are radio, microwave, infrared, visible, ultraviolet, X-ray and gamma; wavelength decreases while frequency and photon energy increase across that order.

Use approximate ranges as scale guides, not as sharp universal borders. Match a region to an application only after checking the relevant wavelength or energy.

Microwaves have shorter wavelengths and higher frequencies than radio waves; X-rays are shorter and more energetic than ultraviolet.

The spectrum is continuous, and region labels are conventions rather than isolated gaps in wavelength.

The visible band is approximately 400–700 nm in free space, from shorter-wavelength violet to longer-wavelength red.

Treat the limits as approximate and use wavelength/frequency trends when identifying colour or neighbouring ultraviolet and infrared.

A 500 nm wave lies in the visible range, while 350 nm is ultraviolet and 900 nm is infrared.

Visible colour is not determined by intensity alone; wavelength sets the nominal colour while intensity affects brightness.

Polarisation restricts oscillations to a preferred direction. Only transverse waves can be polarised because longitudinal oscillations have no sideways direction to select.

Describe the transmission axis and the orientation of the incident electric field. A polariser changes allowed vibration direction, not necessarily frequency.

A polarising filter can reduce light intensity as it is rotated relative to the incoming plane-polarised light.

Polarisation is not the same as reflection, and observing polarisation rules out a purely longitudinal wave.

For plane-polarised light entering an analyser, transmitted intensity is I=I₀ cos²θ, where θ is the angle between the incident polarisation direction and analyser axis.

Use degrees or radians consistently, identify I₀ at θ=0 and remember that an analyser at 90° ideally blocks the light.

At θ=60°, the transmitted intensity is one quarter of I₀ because cos²60°=0.25.

The cosine is squared; using I=I₀cosθ overestimates transmission, and θ is not automatically the angle between two arbitrary filter surfaces.