• Waves are produced by oscillating (vibrating) sources, and they transfer energy away from that source — without transferring matter.
• Key wave quantities: wavelength (λ), amplitude (A), period (T), frequency (f), and wave speed (v).
• f = 1/T — frequency and period are reciprocals of each other.
• The wave equation, v = fλ, links speed, frequency, and wavelength for any wave.
• Transverse waves: particles oscillate perpendicular (at 90°) to the direction of energy transfer. Example: light, water ripples, a guitar string.
• Longitudinal waves: particles oscillate parallel to the direction of energy transfer, creating compressions and rarefactions. Example: sound.
• Only transverse waves can be polarised — longitudinal waves cannot.
• Waves can be represented on displacement-distance graphs (a "snapshot" of the wave) or displacement-time graphs (following one single particle over time).
• Longitudinal waves can also be shown on a pressure-distance graph, which is 90° out of phase with the displacement graph.
• Core Practical 4 uses an oscilloscope and signal generator to measure the speed of sound in air.

Every wave starts with something oscillating — vibrating back and forth around a fixed point. Think of a hand shaking one end of a rope, or a loudspeaker cone vibrating in and out. That oscillation doesn't stay put — it travels outward, away from the source, carrying energy with it but not matter. This is the single most important idea to hold onto: a wave is a travelling disturbance, not a travelling "thing."

Waves can travel through a medium (a physical substance like air, water, or a solid) or, in the case of electromagnetic waves, through a vacuum — empty space with no particles at all. Whether a wave needs a medium or not depends entirely on what type of wave it is, which we'll get to in a moment.

The five quantities you must know cold

Now that you know wavelength, frequency, and speed, they're all connected by one equation that appears constantly throughout this entire course (and beyond — it comes up again in electromagnetic waves, sound, and even quantum physics). Learn it so well you could recite it in your sleep.

Here's the intuition behind it: imagine standing at a fixed point watching a wave pass by. In one second, f complete wavelengths pass you (that's literally what frequency means). Each of those wavelengths is λ metres long. So the total distance the wave has travelled in that one second — which is exactly its speed — is f × λ. That's the whole equation, derived from nothing but the definitions of frequency and wavelength.

Crucially: for a wave travelling at a constant speed (e.g. sound in air at a fixed temperature, or light in a vacuum), if the wavelength goes up, the frequency must go down to compensate — and vice versa. They are inversely proportional when speed is fixed.

In a longitudinal wave, the particles of the medium oscillate parallel to the direction the wave (and its energy) is travelling. Picture pushing and pulling one end of a stretched slinky spring — the coils bunch together and spread apart along the same line that the wave moves down. That's longitudinal motion.

This back-and-forth squeezing creates two characteristic regions:

• Compressions — regions where particles are bunched close together, creating an area of high pressure.
• Rarefactions — regions where particles are spread further apart, creating an area of low pressure.

Examples of longitudinal waves: sound waves, ultrasound waves, and P-waves (primary seismic waves) produced by earthquakes.

In a transverse wave, particles oscillate perpendicular (at 90°) to the direction the wave — and its energy — travels. Think of a rope tied to a wall: if you flick your end up and down, each point on the rope moves vertically, while the wave pattern itself travels horizontally along the rope. Those two directions are at right angles to each other.

Examples of transverse waves: all electromagnetic waves (radio, visible light, UV, X-rays, etc.), vibrations on a guitar string, and ripples on a rope or slinky when shaken sideways.

Waves can be shown on two very different types of graph, and mixing them up is one of the most common exam mistakes. Learn to tell them apart instantly.

Longitudinal waves on graphs

Longitudinal waves are trickier to draw because compressions and rarefactions don't "look" like a wave physically — but they can still be converted into a displacement-distance graph by plotting how far each particle has shifted from its rest position:

• At a compression, particles either side are pushed towards it, so at the compression point itself, displacement = zero (it's a balance point).
• At a rarefaction, particles either side are pulled away from it, so displacement there is also zero.
• Maximum displacement occurs halfway between a compression and a rarefaction.

Longitudinal waves can also be shown on a pressure–distance graph: pressure is highest at compressions and lowest at rarefactions, and this pressure graph is 90° out of phase with the displacement graph (a peak in pressure lines up with a zero-crossing in displacement).

A stationary (standing) wave forms when a wave reflects back on itself with a 180° phase difference, and the original wave overlaps with the reflected one. Instead of the pattern travelling along, it appears to stay in place — creating fixed points called nodes (zero displacement, always) and antinodes (maximum displacement, oscillating up and down).

Stationary waves can be either transverse or longitudinal, and they're plotted on graphs exactly the same way as ordinary travelling waves. The key thing to remember is that one full wavelength only makes up a portion of the total length of the string — don't assume the string length equals one wavelength.

Aim

To measure the speed of sound in air between two points, using an oscilloscope and a signal generator connected to a loudspeaker and microphone.

Variables

• Independent variable: distance between microphone and loudspeaker
• Dependent variable: phase of the received signal (compared to the transmitted one)
• Control variables: same location, same microphone, and a fixed frequency for each set of readings

Equipment

• Signal generator with loudspeaker
• Oscilloscope with 2-beam facility
• Microphone
• 2 metre rulers (or a measuring tape ≥ 2 m)
• Connecting leads

Method — in plain steps

1. Connect the microphone and signal generator to the oscilloscope. Place the generator about 50 cm from the microphone, and set the signal to roughly 4 kHz.
2. Adjust the oscilloscope's time base so both the generator's signal and the microphone's signal appear on screen together, showing about three cycles.
3. Adjust the distance between microphone and speaker so that a trough on the upper trace lines up exactly with a peak on the lower trace — this alignment is much easier to judge accurately than trying to line up matching peaks.
4. Record this first distance between the microphone and the signal generator.
5. Slowly move the microphone further away, watching the two traces on the screen.
6. When the next trough-peak alignment occurs, record the new distance.
7. Repeat this "move and record" process as many times as the available space allows.
8. Calculate the mean wavelength from the set of distances collected (each successive alignment distance represents one wavelength apart).
9. Read the frequency directly off the oscilloscope trace (using the time base), rather than trusting the signal generator's dial.
10. Repeat the whole process at roughly half the original frequency (~2 kHz) for a second data set.

Evaluating the experiment

Systematic errors: Make sure the oscilloscope's time-base scale is read correctly (it's often in milliseconds, easy to misread) — always calculate frequency from the trace itself rather than relying on the signal generator's dial, which may not be perfectly accurate.

Random errors: Take repeat readings and average them to reduce random error. Since the distances involved are small, keep the microphone-to-speaker separation as large as practically possible to reduce the relative size of any measurement uncertainty.

Safety

• Voltage and current are low, so normal electrical safety precautions (e.g. checking leads for damage) are sufficient.
• Keep the sound at a normal listening volume to protect hearing.

• I can define wavelength, amplitude, period, and frequency, and identify each on a graph.
• I can use f = 1/T to convert between frequency and period.
• I can use v = fλ to solve for any one of speed, frequency, or wavelength, including unit conversions.
• I can explain the difference between transverse and longitudinal waves in terms of particle oscillation direction.
• I can give at least two real-world examples of each wave type.
• I know that only transverse waves can be polarised, and can explain why.
• I can identify compressions and rarefactions on a longitudinal wave diagram.
• I can tell the difference between a displacement-distance graph and a displacement-time graph, and know what each one lets me measure.
• I understand that a sinusoidal graph shape alone does NOT tell me whether a wave is transverse or longitudinal.
• I can convert a longitudinal wave into a displacement-distance representation, and relate it to a pressure-distance graph.
• I can identify nodes and antinodes on a stationary wave diagram, and know their spacing is λ/2.
• I can describe the full method for Core Practical 4 (measuring the speed of sound), including safety and error evaluation.