Properties of waves & RP8 — AQA GCSE Physics

SPEC 4.6.1.2 • WAVE PROPERTIES & RP8

Wave Equations & RP8

Two equations: v = fλ (recall) and T = 1/f (equation sheet). Plus RP8 — measuring waves in a ripple tank and on a stretched string. Calculation marks are the easiest in Paper 2 if you get the units right.

Wave Speed (v)

Lesson 6.01 gave you the four wave properties — λ, amplitude, f, T. Now we add one more: wave speed, and link it to frequency and wavelength.

Wave Speed [DEF]

The speed at which the energy is transferred (or the wave moves) through the medium. Measured in metres per second (m/s).

What Determines Wave Speed

Wave speed depends on the medium, not on the source. Sound travels at ~340 m/s in air, ~1500 m/s in water, ~5000 m/s in steel. Light travels at 3.0 × 10⁸ m/s in a vacuum.

Increasing the loudness of a sound (bigger amplitude) does not change its speed. Same wave, same medium → same speed.

The Wave Equation

The most important equation in Module 6. AQA expects you to recall this — it is not on the equation sheet.

v = f × λ

wave speed (m/s) = frequency (Hz) × wavelength (m)

What It Means

If a wave's frequency is the number of waves per second, and each wave is λ metres long, then in one second the wave travels f × λ metres. That distance per second is the speed.

Rearrangements You'll Need

f = v / λ (find frequency given speed and wavelength) | λ = v / f (find wavelength given speed and frequency). The triangle trick works: cover the unknown.

Worked Example 1

A musical note has a frequency of 256 Hz. The sound wave in air has a wavelength of 1.3 m.

Calculate the speed of the sound wave. 3 marks

E

v = f × λ

S

v = 256 × 1.3

U

metres per second (m/s)

A

v = 332.8 m/s ≈ 333 m/s

Mark scheme: 1 mark for correct equation, 1 mark for substitution, 1 mark for correct answer with unit. Both 332.8 and 333 m/s would be accepted (allow correct rounding).

Worked Example 2 — Conversion Trap

A radio station broadcasts at a frequency of 95 MHz. Radio waves travel at 3.0 × 10⁸ m/s.

Calculate the wavelength of the radio wave. Give your answer to 2 significant figures. 3 marks

E

v = f × λ → rearrange to λ = v / f

S

Convert first: f = 95 MHz = 95 × 10⁶ Hz

λ = (3.0 × 10⁸) / (95 × 10⁶)

U

metres (m)

A

λ = 3.157… m ≈ 3.2 m

The killer step: if you substitute 95 (not 95 × 10⁶), your answer comes out a million times too big. Always convert prefixes (MHz, kHz, mm, cm) to base SI units before substituting.

Period & Frequency Link

Period and frequency are reciprocals of each other. This equation is on the equation sheet — you don't need to recall it, but you do need to use it.

T = 1 / f

period (s) = 1 / frequency (Hz)

Quick Sanity Check

A wave at 50 Hz has period T = 1/50 = 0.02 s (20 ms). A wave at 1 Hz has period T = 1 s. High frequency = short period, and vice versa.

Q: A wave on a string has a period of 8.0 ms. Calculate its frequency. 2 marks

E

T = 1 / f → f = 1 / T

S

Convert: T = 8.0 ms = 0.0080 s. f = 1 / 0.0080

U

hertz (Hz)

A

f = 125 Hz

RP8 — Required Practical 8

RP8 is the wave practical. The spec specifies two methods in one practical: a ripple tank for waves in a fluid, and a stretched string for waves in a solid.

RP8 Aim

"Make observations to identify the suitability of apparatus to measure the frequency, wavelength and speed of waves in a ripple tank and waves in a solid."

What You're Measuring

Frequency (f) — read from the signal generator, or by counting waves passing a point per second

Wavelength (λ) — measured with a ruler (different technique in each setup)

Wave speed (v) — calculated using v = fλ, or measured directly with distance ÷ time

RP8 (A) — Ripple Tank

Water waves are generated by a vibrating dipper; a lamp casts the wave pattern onto paper below so it can be measured.

Method

Set the frequency on the signal generator driving the dipper — this gives you f directly.

Measure the wavelength: project the wave pattern onto paper below the tank, then use a ruler to measure the distance across several wavelengths (e.g. 5 wavelengths) and divide by that number — this reduces measurement uncertainty.

Calculate the wave speed using v = fλ.

Ripple Tank — Measuring v Directly

You can also measure wave speed without using v = fλ: just time how long a wave takes to cross a known distance.

Direct Speed Measurement

Mark two points on the tank a known distance apart (use a metre rule).

Start a stopwatch as a wavefront crosses the first mark; stop it as it crosses the second.

Speed = distance ÷ time.

Repeat the timing several times and take a mean — this reduces random error.

Why Repeat?

Mark scheme phrasing (Jun 2021 Q06.1, 1 mark): "to reduce the effect of random errors". Don't write "to be more accurate" or "to get a better result" — examiners reject vague phrasing. Use the words random errors.

Alternative — Stroboscope

A stroboscope flashing at the same frequency as the waves makes them appear stationary. This makes wavelength much easier to measure with a ruler — the moving pattern would otherwise be blurry.

RP8 (B) — Stretched String

For waves in a solid: a vibration generator drives one end of a horizontal string; the other end runs over a pulley with masses attached to keep it taut.

Method

Hang masses on the string over the pulley to set the tension.

Adjust the signal generator frequency slowly until a clear standing wave appears — the string vibrates in stationary "loops".

Read f from the signal generator display.

Measure the wavelength: λ = 2 × distance between adjacent nodes (a "node" is where the string is stationary). Use a metre rule.

Calculate v = fλ.

Method — Speed Of Sound In Air

A separate spec requirement (4.6.1.2): "describe a method to measure the speed of sound waves in air". Don't confuse this with RP8 (which is ripple tank + string).

Standard Method — Two Microphones + Oscilloscope

Place two microphones a measured distance d apart in a straight line from the sound source.

Connect both microphones to a dual-trace oscilloscope.

Make a sharp sound (e.g. clap) at one end. Each microphone picks up the sound, producing two traces on the oscilloscope, slightly offset in time.

Read the time difference t between the two traces from the oscilloscope.

Speed of sound = d ÷ t.

Simpler Alternative — Echo Method

Stand a known distance d from a tall wall. Clap and time the interval t between the clap and the returning echo. The sound travels 2d (there and back), so speed = 2d ÷ t. Less precise but accepted at GCSE.

Expected Value

Speed of sound in air at room temperature is approximately 340 m/s. Any answer in the range 320–360 m/s is reasonable.

Sound Across Media PHYSICS ONLY

A final spec point for physics students (not in combined science): when a sound wave passes from one medium to another — say from air into water — what happens to v, f, and λ?

The Rule

Frequency (f) stays the same — it is set by the source (the thing producing the sound). The medium can't change it.

Wave speed (v) changes — it depends on the medium. Sound travels faster in denser materials: ~340 m/s in air, ~1500 m/s in water, ~5000 m/s in steel.

Wavelength (λ) must change — since v = fλ and f is fixed, if v increases then λ must increase too.

Worked Example

A whale produces a sound at 400 Hz. In air, this gives a wavelength of 0.85 m (since v ≈ 340 m/s). What happens in water (v ≈ 1500 m/s)?

f is unchanged at 400 Hz. v rises to 1500 m/s. So λ = v/f = 1500/400 = 3.75 m — a much longer wavelength in water. Same source, same frequency, different medium → different speed → different wavelength.

Trap

Students often say "the frequency changes when sound enters water". It doesn't. The source's vibration rate doesn't depend on what medium the wave travels into. Only v and λ change.

Examiner Alert

From Jun 2024 P2 Q4.5

95% of students scored at least 2 of 3 marks on a v = fλ wavelength calculation. The lost mark was almost always the same: not converting units before substituting.

Examiner reports consistently flag this. Frequencies in MHz or kHz, wavelengths in cm or mm, periods in ms — all need converting to SI before the calculation starts.

Conversion Cheat Sheet

QuantityConvert fromTo SI

Frequency1 MHz1 × 10⁶ Hz

Frequency1 kHz1 × 10³ Hz

Wavelength1 cm0.01 m (1 × 10⁻² m)

Wavelength1 mm0.001 m (1 × 10⁻³ m)

Period1 ms0.001 s (1 × 10⁻³ s)

Period1 μs1 × 10⁻⁶ s

Weak Vs Strong — Calculation Answer

Same question, two answers. One scores 1/3, the other scores 3/3.

"Calculate the wavelength of a sound wave with frequency 4.0 kHz, travelling at 340 m/s." (3 marks)

Weak — 1/3 marks

Working:

λ = v / f

λ = 340 / 4.0

λ = 85 m

Why it fails: 4.0 kHz substituted as 4.0 Hz. Answer is 1000× too big. 1 mark for the equation only.

Strong — 3/3 marks

Working:

λ = v / f

Convert: f = 4.0 kHz = 4000 Hz

λ = 340 / 4000

λ = 0.085 m (or 8.5 cm)

Why it works: Conversion shown explicitly. Equation, substitution, answer with unit — all three marks.

Common Errors

Students often writeCorrect versionWhy it matters

Substitutes without converting (e.g. f in MHz, λ in mm)Convert before substituting; show the conversion lineAnswer is off by a factor of 10ⁿ — typically the lost mark

"To get a more accurate result" (when asked why you repeat)"To reduce the effect of random errors "Vague phrasing rejected by mark schemes (Jun 2021 06.1)

Measures only one wavelength on the ripple tankMeasure across several wavelengths and divideReduces uncertainty — better resolution from the ruler

λ on a stretched string = node-to-node spacingλ = 2 × node-to-node spacing (one node to the next-but-one )Off by factor of 2 — common silent error

"Bigger amplitude = faster wave"Wave speed depends on the medium , not the amplitudeConceptual mistake — louder ≠ faster

Practice Question

A student investigates waves on a stretched string. The signal generator drives the vibrator at 120 Hz. A clear standing wave forms with three loops between the fixed bridge and the vibrator. The total distance between the bridge and the vibrator is 0.60 m.

(a) Calculate the wavelength of the wave. 2 marks

(b) Calculate the wave speed. 2 marks

(c) The student then increases the tension by adding more masses. The same 120 Hz frequency now shows only two loops in the same length of string. State whether the wave speed has increased, decreased or stayed the same, and justify your answer using v = fλ. 2 marks

(a) Three loops = 1.5 full wavelengths in 0.60 m. So λ = 0.60 / 1.5 = 0.40 m.

(Alternative: each loop = ½ wavelength. 3 loops × ½ = 1.5 λ in 0.60 m → λ = 0.40 m.)

(b) v = fλ = 120 × 0.40 = 48 m/s.

(c) Two loops in 0.60 m means λ = 0.60 / 1 = 0.60 m (longer). Since f is unchanged at 120 Hz: v = fλ = 120 × 0.60 = 72 m/s. Wave speed has increased — because tension affects the speed at which waves travel in the string.

ESUA Structure — Why It Earns Marks

Calculation marks come in three steps almost every time: Equation, Substitution, Answer with correct unit. The "U" reminder makes sure you don't drop the unit at the end.

The Four-Letter Discipline

E — Equation: write the equation in symbols (even if it's on the equation sheet). Examiners credit this as a separate mark on most 3-mark calculations.

S — Substitute: convert any non-SI units on this line , then substitute. Show the conversion explicitly.

U — Unit: state the SI unit you expect the answer in (m/s, Hz, s, m). Forgetting this drops a mark.

A — Answer: calculate to a sensible number of significant figures (2 or 3). Include the unit again.

If You Get The Wrong Numerical Answer

You can still score 2/3 marks even with the wrong final number — if the equation and substitution are correct. This is "ECF" (error carried forward). Always write the equation and the substitution line; don't just write a number.

Lesson Summary

You've finished Lesson 6.02. Tick yourself off against the spec checkpoints below before moving on.

v = fλ

Recall — m/s

T = 1/f

Equation sheet — s

RP8

Ripple tank + string

✓ Checkpoint — You Can Now…

Define wave speed and state its unit (m/s)

Apply v = fλ in any direction (find v, f, or λ) with correct unit conversions

Apply T = 1/f to convert between period and frequency

Describe the ripple tank method for f, λ, v of water waves

Describe the stretched string method, including λ = 2 × node-to-node spacing

Describe a method to measure the speed of sound in air (two-microphone or echo)

(Physics only) Explain that when sound moves between media, f stays the same , v and λ both change

State why we repeat measurements: to reduce random errors

Convert MHz → Hz, kHz → Hz, mm → m, ms → s before substitution

Next Up

Lesson 6.03 — Reflection of waves and sound (physics-only, HT). The reflection law applies to all wave types.