Sound

The echo calculation is the trap in sound: the distance doubles and half of all candidates forget. This subtopic mixes easy recall (pitch, loudness, the hearing range) with one calculation that Cambridge sets in some form most sessions.

What are the key facts about sound waves?

Sound is produced by vibrating sources and travels as a longitudinal wave: the air particles vibrate parallel to the direction of travel, forming compressions and rarefactions. Sound needs a medium. It cannot travel through a vacuum, and the bell-in-a-vacuum-jar demonstration is the standard evidence.

Fact	Value
Human hearing range	20 Hz to 20 000 Hz (20 kHz)
Speed of sound in air	approximately 330-350 m/s
Ultrasound	frequency above 20 kHz

Speed depends on the medium. Sound travels fastest in solids, slower in liquids and slowest in gases, because particles in solids are closest together and pass vibrations on most quickly (Extended detail). Light travels almost a million times faster than sound, which is why thunder arrives seconds after lightning, a fact examiners use in distance-estimate questions.

Two wave properties control what you hear. Pitch depends on frequency: higher frequency means higher pitch. Loudness depends on amplitude: larger amplitude means louder sound. On an oscilloscope trace, a louder sound shows taller waves; a higher-pitched sound shows more waves squeezed into the same time.

How do you do an echo calculation without losing marks?

Double the distance: in any echo problem the sound travels there and back, twice the distance to the reflecting surface. Use $\text{speed} = \text{distance} \div \text{time}$, in symbols $v = \dfrac{s}{t}$, then halve or double at the right point. Decide before substituting: does the time given cover one way or the round trip? Write “total distance $= 2d$” on the page first. Ultrasound applications use the same idea: sonar depth-finding at sea, medical scanning of a foetus, and detecting flaws inside metal all time a reflected pulse.

Worked Exam Question

A student stands 660 m from a cliff and claps. She hears the echo 4.0 s later. Calculate the speed of sound in air. [3]

Worked solution:

1. Total distance travelled by the sound $= 2 \times 660 = 1320\ \text{m}$ (to the cliff and back)
2. Equation: $v = s \div t$
3. Substitute: $v = 1320 \div 4.0$
4. Answer: $v = 330\ \text{m/s}$ (2 significant figures)

Mark scheme:

• M1: doubling the distance: $2 \times 660 = 1320\ \text{m}$
• M1: $v = s \div t$ with candidate’s distance substituted
• A1: $330\ \text{m/s}$ with unit (165 m/s scores M1 only)

Common Mistakes

• Forgetting to double the distance in echo problems. The answer 165 m/s is the examiner’s planted wrong value. If your speed of sound is near 165, you halved when you should not have.
• Saying loudness depends on frequency, or pitch on amplitude. Pair them correctly: pitch with frequency, loudness with amplitude.
• Claiming sound travels through a vacuum, or fastest in gases. It needs particles and is fastest in solids.
• Describing sound as transverse. It is longitudinal; the compression and rarefaction structure is the evidence.
• Reading an oscilloscope trace as if the horizontal axis were distance. It is time, so count waves per division to compare frequencies.

Exam Technique Tip

Open every echo or sonar answer with a one-line sketch: source, reflector, and a double-headed arrow labelled $2d$. The sketch takes ten seconds and makes the doubling step impossible to miss. Then run the standard routine (equation, substitute, answer with unit) so the method marks survive any arithmetic slip.

How This Is Examined

Sound runs through every paper. Papers 1 and 2 test the hearing range, oscilloscope-trace comparisons and one-step speed calculations. Papers 3 and 4 carry echo calculations and describe questions on producing and transmitting sound; Extended (Paper 4) adds the solid, liquid and gas speed comparison with a particle explanation and harder multi-step sonar problems. Papers 5 and 6 occasionally use a measure-the-speed-of-sound method (two students, a stopwatch and a known distance) and ask about timing errors. The doubling rule is a habit, not a talent. Most students stop forgetting it after roughly ten drilled examples in a 1-to-1 class.