These twelve questions cover the order and uses of the spectrum, safety, sound in different media, echoes, pitch and loudness from electromagnetic spectrum and sound. All data is invented for practice and is not taken from any exam paper. They go from easier to harder.
Write your answer with its unit on paper first, then open the answer. Use 3.0 × 10⁸ m/s for electromagnetic waves, 330 m/s for sound in air, 1500 m/s in water and 5000 m/s in steel unless told otherwise. Round with care, and the bounds and rounding explainer shows how to state a sensible precision.
Questions
1. Which has the highest frequency: radio waves, X-rays or infrared?
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X-rays. The order from lowest to highest frequency is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
2. A radio station broadcasts at 1.0 × 10⁸ Hz. Find the wavelength.
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λ = v ÷ f = 3.0 × 10⁸ ÷ 1.0 × 10⁸ = 3.0 m. Check: 1.0 × 10⁸ × 3.0 = 3.0 × 10⁸.
3. Name the region of the spectrum that suits each use: (a) heating food, (b) checking a security mark on a banknote, (c) imaging a broken bone.
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(a) Microwaves, because water in food absorbs them. (b) Ultraviolet, because the mark glows (fluoresces) under it. (c) X-rays, because bone absorbs more than soft tissue.
4. A dental worker wears a lead apron and leaves the room while an X-ray is taken. Explain why.
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X-rays can damage or mutate cells and may cause cancer. The worker takes many X-rays, so exposure adds up. Lead absorbs X-rays, and leaving the room reduces the time and dose received.
5. You see a flash of lightning and hear the thunder 4.0 s later. How far away is the lightning? Ignore the time taken by light.
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Distance = 330 × 4.0 = 1320 m. The time for light, about 4.4 × 10⁻⁶ s, is negligible. Check: 1320 ÷ 330 = 4.0 s.
6. A sound travels 1000 m through steel and another 1000 m through air. Find the time for each.
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Steel: 1000 ÷ 5000 = 0.20 s. Air: 1000 ÷ 330 = 3.03, so 3.0 s (2 significant figures). The sound is about 15 times faster in steel.
7. A clap is heard as an echo 0.40 s later from a wall. How far away is the wall?
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Total path = 330 × 0.40 = 132 m. Distance = 132 ÷ 2 = 66 m.
8. A sonar pulse is sent to the sea bed 450 m below a boat. How long until the echo returns?
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Total path = 2 × 450 = 900 m. Time = 900 ÷ 1500 = 0.60 s.
9. A student stands 85 m from a wall and measures 0.50 s between a clap and its echo. Calculate the speed of sound.
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Total path = 2 × 85 = 170 m. Speed = 170 ÷ 0.50 = 340 m/s.
10. On an oscilloscope, 4 complete waves occupy 20 ms. Find the period and the frequency.
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T = 20 ms ÷ 4 = 5.0 ms = 0.0050 s. f = 1 ÷ 0.0050 = 200 Hz.
11. Sound A has amplitude 2.0 cm on a trace and frequency 400 Hz. Sound B has amplitude 1.0 cm and frequency 800 Hz. Compare their pitch and loudness.
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B has the higher frequency, so it has the higher pitch. A has the larger amplitude, so A is louder. Pitch and loudness are separate properties.
12. A cleaner uses ultrasound of frequency 40 kHz in air. (a) Can a person hear it? (b) Find its wavelength. (c) Explain why ultrasound cannot be used to send a message from a spacecraft to Earth.
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(a) 40 kHz = 40 000 Hz, above the approximate hearing limit of 20 000 Hz, so no.
(b) λ = v ÷ f = 330 ÷ 40 000 = 0.00825 m, about 8.3 mm (0.0083 m). Check: 40 000 × 0.00825 = 330.
(c) Sound needs particles to pass on the vibration, and space is close to a vacuum. A radio wave is electromagnetic and crosses it.
If you got these wrong
Match the kind of error to the lesson that fixes it.
- Order of regions, wavelength or frequency (1, 2) and matching uses (3): return to placing a use within a spectrum region.
- Vague safety wording (4): return to explaining a safety consideration without sensationalism.
- Speeds in different media, or vacuum (6, 12c): return to comparing sound travel in different media.
- Answers double or half the expected value (5, 7, 8, 9): return to using echo timing with a return journey. Draw the path first. Question 5 is a one-way journey, so do not halve it.
- Pitch, loudness, period and frequency (10, 11, 12a, 12b): return to interpreting pitch and loudness separately.
Log any repeated slip in the mistake log and retest queue and retry a fresh version a few days later. If the same error keeps returning, online one-to-one Physics tuition lets a teacher watch the step where it happens.