10 AQA GCSE Physics questions on period and frequency (T = 1/f) that get harder as you go, from Foundation to Higher, each with a full worked solution.
Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Equation sheet: given in the exam
📌 KEY DEFINITIONS – learn them word for word
Period: the time taken for one complete wave to pass a point. Unit: seconds (s).
Frequency: the number of waves passing a point each second. Unit: hertz (Hz). 1 Hz = 1 wave per second.
The equation
period = 1 ÷ frequency T = 1 / f
| Quantity | Symbol | Unit |
|---|---|---|
| period (time for one wave) | T | seconds (s) |
| frequency (waves per second) | f | hertz (Hz) |
Rearranged: f = 1 ÷ T | 1 ms = 0.001 s; 1 kHz = 1000 Hz
Use FIFA for every answer
- F – Formula: write the equation as it appears on the sheet.
- I – Insert: put in the numbers (convert to standard units first).
- F – Fix: rearrange to make the unknown the subject.
- A – Answer: calculate and always give the unit.
Foundation: aim for Q1–8. Higher: aim for Q4–10. Most questions need rearranging.
Questions
Q1 (F) A wave in a ripple tank has a frequency of 5 Hz. Calculate its period.
Show solution
F: T = 1 / f
I: T = 1 ÷ 5
F: T is already the subject
A: 0.2 s
Q2 (F) A buoy bobs up and down once every 4 s. Calculate the frequency of the waves.
Show solution
F: T = 1 / f
I: 4 = 1 ÷ f
F: f = 1 ÷ 4
A: 0.25 Hz
Q3 (F) UK mains electricity has a frequency of 50 Hz. Calculate the period of one cycle.
Show solution
F: T = 1 / f
I: T = 1 ÷ 50
F: T is already the subject
A: 0.02 s
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Q4 (F) A guitar string vibrates with a period of 2.5 ms. Calculate its frequency.
Show solution
Convert first: 2.5 ms = 0.0025 s
F: T = 1 / f
I: 0.0025 = 1 ÷ f
F: f = 1 ÷ 0.0025
A: 400 Hz
Q5 (F) A dog whistle produces sound at 25 kHz. Calculate the period in ms.
Show solution
Convert first: 25 kHz = 25 000 Hz
F: T = 1 / f
I: T = 1 ÷ 25 000 = 0.000 04 s
F: × 1000 to get ms
A: 0.04 ms
Q6 (F/H) A student counts 12 waves passing a post in 3.0 s. Calculate the period of the waves.
Show solution
Frequency: f = 12 ÷ 3.0 = 4 Hz
F: T = 1 / f
I: T = 1 ÷ 4
F: T is already the subject
A: 0.25 s
Q7 (F/H) A resting heart beats 72 times per minute. Calculate the time between beats, to 2 significant figures.
Show solution
Frequency: f = 72 ÷ 60 = 1.2 Hz
F: T = 1 / f
I: T = 1 ÷ 1.2
F: T = 0.833… s
A: 0.83 s (2 s.f.)
Q8 (F/H) A radio wave has a frequency of 1.0 × 108 Hz. Calculate its period.
Show solution
F: T = 1 / f
I: T = 1 ÷ 1.0 × 108
F: T is already the subject
A: 1.0 × 10−8 s
Q9 (H) Sea waves have a period of 5.0 s and a wavelength of 40 m. Calculate their speed.
Show solution
Step 1 – frequency
F: T = 1 / f
I: 5.0 = 1 ÷ f
F: f = 1 ÷ 5.0 = 0.2 Hz
Step 2 – speed
F: v = f λ
I: v = 0.2 × 40
A: 8 m/s
Q10 (H) On an oscilloscope, one complete wave covers 3.5 divisions. The time-base is set to 2 ms per division. Calculate the frequency, to 2 significant figures.
Show solution
Period: T = 3.5 × 2 ms = 7 ms = 0.007 s
F: T = 1 / f
I: 0.007 = 1 ÷ f
F: f = 1 ÷ 0.007 = 142.9 Hz
A: 140 Hz (2 s.f.)
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