7.1 Progressive 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.