Sound waves, decibels and the loudest sound ever recorded
The wave equation, how temperature changes the speed of sound, the logarithmic decibel scale, and what the 1883 Krakatoa records tell us. With an echo experiment to measure the speed of sound.
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Sound is a longitudinal pressure wave: a disturbance of matter transmitted outward from its source, made of compressions and rarefactions. Like all waves it obeys v = f·λ, where v is the wave speed, f the frequency and λ the wavelength. The human audible range is roughly 20 Hz to 20,000 Hz.[1][2]
In air the speed of sound depends on temperature: v = 331 m/s × √(T / 273 K), with T in kelvin. At 20 °C (293 K) this gives about 343 m/s. In fresh water sound travels at about 1480 m/s and in steel at about 5960 m/s.[2]
Sound needs a medium. Most of space is essentially a vacuum, so sound waves cannot travel there, although the hot gas inside galaxy clusters is dense enough to carry very low-frequency pressure waves.[5]
Loudness is measured on the logarithmic decibel scale: β = 10·log₁₀(I / I₀), with I₀ = 10⁻¹² W/m² (the threshold of hearing). Every +10 dB means 10 times the intensity: a 90 dB sound is 1000 times as intense as a 60 dB one. Typical values: whisper 20 dB, conversation 60 dB, threshold of pain 120 dB, jet at 30 m 140 dB, eardrums burst at about 160 dB.[3]
In August 1883 the volcano Krakatoa exploded. A barometer at the Batavia gasworks, about 160 km away, jumped by more than 2.5 inches of mercury, a pressure spike equal to more than 172 dB. On the ship Norham Castle, about 64 km away, the captain wrote that the eardrums of over half his crew had been shattered.[4]
The explosion was heard on Rodrigues island, about 4,800 km away. Long after it was too quiet to hear, barometers around the world kept recording the pressure wave as it went round the globe three to four times in each direction.[4]
Try it: Measure the speed of sound with an echo
You need
- A large flat wall (a school building) with open ground in front
- A measuring tape or trundle wheel
- Two wooden blocks to clap together
- A stopwatch (or a phone)
Safety
Choose a place away from traffic. Keep clapping blocks away from fingers. Do not use starting pistols or anything explosive.
What to do
- Stand at least 50 m from the wall. Measure the distance d to the wall.
- Clap the blocks once and listen for the echo.
- Now clap steadily so that each clap is made exactly when you hear the echo of the previous one. Practise the rhythm.
- A partner times 20 claps (start counting at zero). Repeat three times.
- Between two claps the sound travels to the wall and back, a distance of 2d. Time per clap t = (total time) ÷ 20.
- Calculate v = 2d / t. Compare with 331 × √(T/273) for today's air temperature.
What happens, and why?
The echo method uses a long path and many repetitions to make reaction-time errors small. Your result should be within about 10% of 340 m/s. Warmer air gives a slightly higher speed, as v = 331·√(T/273 K) predicts.[2]
Play: Decibel ladder
Put each sound, or each calculation, on the right rung of the decibel ladder. Remember: +10 dB is 10 times the intensity.
Your best score is kept only on this device. Nothing is sent anywhere.
Quiz
Other ages: Ages 6–7 · Ages 10–11