AeroLab Reading room

Physics / AS level

Waves

Describe phase, intensity and the Doppler effect.

Learning objectives

The big idea

A progressive wave carries energy while points of the medium oscillate around equilibrium. Phase describes position within a cycle; points separated by one wavelength are in phase.

Intensity is power per unit area and is proportional to amplitude squared for a fixed wave system. Relative motion between source and observer changes the observed frequency through the Doppler effect, even when the source frequency is unchanged.

1. Describe an oscillation and its travel separately

A progressive wave joins local oscillations into a moving pattern. A point’s displacement changes with time, while a crest moves through space. Phase identifies position in a cycle: points one wavelength apart on a simple progressive wave have phase difference 2π, and points half a wavelength apart differ by π. A phase difference must refer to specified points or specified times, not simply to two arbitrary arrows.

2. Frequency, speed and intensity

Frequency is set by the source; wave speed depends on the medium and conditions. At a stationary boundary, a speed change therefore changes wavelength while frequency remains fixed. Intensity is power per area and scales with amplitude squared for an unchanged wave system. Doubling amplitude gives four times the intensity under those conditions. The proportionality alone does not compare unrelated waves with different media, frequencies or detector responses.

3. Longitudinal and transverse mechanisms

In transverse motion, displacement is perpendicular to propagation; in longitudinal motion it is parallel. Sound in air involves pressure and density variations, not a sequence of particles flying from source to listener. Polarisation restricts transverse oscillation directions and provides evidence for transverse behaviour. A simple longitudinal pressure wave cannot be plane-polarised in the same way. Electromagnetic waves require no material medium, unlike ordinary sound.

4. Explain a Doppler shift with wavefront spacing

When a sound source approaches a stationary observer, successive wavefronts are emitted from positions closer to that observer. They arrive more frequently even though the source’s own oscillation frequency has not increased. Wavefront spacing is larger behind the receding source. Apply any Doppler equation with the stated source/observer conditions and sign convention; a sound-in-air formula should not be applied unchanged to cosmological redshift or all electromagnetic situations.

A method you can reuse

  1. Label the oscillation direction and propagation direction.
  2. Find frequency, period and wavelength without mixing time and distance graphs.
  3. Convert phase differences into fractions of a cycle.
  4. For intensity ratios, state what remains unchanged.
  5. For Doppler problems, identify which object moves relative to which medium.
Why can an approaching siren sound higher in pitch without emitting higher-frequency oscillations?

Its motion compresses the spacing of wavefronts reaching the observer, increasing their arrival rate. The source frequency and the observed frequency describe different measurements.

Equations and relationships

v=fλv=f\lambda

Wave equation.

Δϕ=2πΔxλ\Delta\phi=\frac{2\pi\Delta x}{\lambda}

Phase difference in radians along a progressive wave.

I∝A2I\propto A^2

Intensity scales with amplitude squared under unchanged conditions.

Worked example

A wave’s amplitude doubles. What happens to its intensity under the same conditions?

Follow the solution

I ∝ A², so the factor is 2² = 4.

Investigate and explain

Pause a travelling wave and compare pairs of points separated by half a wavelength and a whole wavelength.

Track one particle and one wavefront before comparing phase and superposition. These particular tools are related wave models, not a complete moving-source Doppler demonstration.

Open the interactive investigation

Check your understanding

1. What is the phase difference for a path difference of λ/2?

  1. 0 radians
  2. π radians
  3. 2π radians
Check the answer and reasoning

π radians

Half a cycle corresponds to π radians.

2. A wave’s amplitude doubles. What happens to its intensity under the same conditions?

  1. It doubles.
  2. It halves.
  3. It becomes four times as large.
Check the answer and reasoning

It becomes four times as large.

I ∝ A², so the factor is 2² = 4.

3. For sound, what does an approaching source usually do to observed frequency?

  1. It increases the observed frequency.
  2. It reduces the source’s emitted frequency.
  3. It makes the wavelength at the source infinite.
Check the answer and reasoning

It increases the observed frequency.

Successive wavefronts reach the observer closer together.