An acoustic stopwatch measures the time between two sound events, by dating on an audio recording the instant when the signal exceeds a threshold. A smartphone’s microphone provides an excellent one, with a resolution of about 23 µs at 44,100 Hz.
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How to measure it in class
FizziQ offers two approaches: the Triggers tool (Tools menu), which automatically measures the time between two threshold crossings of the sound level, and the oscillogram, on which the instant of each sound burst can be read directly.
Steps:
- Open the Triggers tool and select the sound trigger, or start an audio recording and work afterwards on the oscillogram
- Set the trigger threshold above the room’s background noise, but below the amplitude of the sounds to be dated: too low a threshold fires on a scraping chair, too high a threshold misses the first event
- Produce two short, sharp sounds (two hand claps, two ruler impacts, a marble falling then bouncing): the sharper the attack, the more precise the timing
- Read the displayed time Δt, or measure the gap between the two fronts on the oscillogram
- Repeat the measurement 5 to 10 times and take the average, then estimate the spread
- If the two sounds do not originate at the same place, correct for the propagation time between each source and the microphone
Scientific activities on this topic
- Measuring the speed of sound with two acoustic stopwatches - date the same clap on two smartphones a known distance apart and deduce v
- Measuring your reaction time with the sound stopwatch - build a stopwatch from the triggers and compare human timing with automatic timing
Learn more
What exactly is being dated
An acoustic stopwatch does not measure the instant of the physical event, but the instant when the sound wave produced by that event reaches the microphone. The two coincide only if the source is very close to the mic. This is the main misconception about the method. In a speed-of-sound experiment with two phones 20 m apart, this delay is precisely the quantity being measured; in a falling-marble experiment, it becomes a bias that must either be made negligible (mic 10 cm from the impact, that is 0.3 ms) or subtracted.
Where the resolution comes from
The audio signal is digitized at regular intervals, at the sampling frequency fₛ. The usual values are 44,100 Hz (the CD standard) and 48,000 Hz. The date of a sample is known to within 1/fₛ, that is 22.7 µs at 44.1 kHz and 20.8 µs at 48 kHz. Shannon’s sampling theorem requires fₛ > 2 f_max; with 44.1 kHz, the whole audible spectrum up to 20 kHz is covered. This frequency, originally chosen for musical fidelity, incidentally provides a remarkable clock.
Why it beats a handheld stopwatch
A teenager’s visual reaction time is of the order of 0.20 to 0.25 s. In manual timing, this delay exists at the start and at the finish: it partially cancels out, but its fluctuation from one trial to the next, about 30 to 50 ms, remains irreducible. Over a duration of 0.5 s, that is already 10% uncertainty. The acoustic stopwatch simply removes the operator from the measurement chain.
The smartphone’s own limitations
Three effects degrade the measurement. Reverberation: in a closed room, the echo off the walls can re-trigger the threshold and create a false second event; outdoors or a furnished room is preferable. Audio compression: some formats smooth out transients; record uncompressed whenever possible. Finally, if you use two phones, their clocks are not synchronized with each other - hence the need, in that case, for a protocol that only uses differences measured on the same device, or a shared synchronization signal.
A very old principle
Dating an event by the sound it produces is the oldest acoustic measurement method. As early as 1738, the Paris Academy of Sciences measured the speed of sound by timing the interval between the flash of a cannon and the detonation heard several kilometers away - exactly the principle of the acoustic stopwatch, with a pendulum in place of the sound card. Counting the seconds between lightning and thunder to estimate the distance of a storm is the popular version, with the rule of 3 seconds per kilometer.
Formula
Time between two events dated on the audio track, at samples n₁ and n₂:
Δt = (n₂ − n₁) / fₛ
Temporal resolution of the measurement:
δt = 1 / fₛ
Propagation-time correction, when the two sources are at distances d₁ and d₂ from the microphone:
Δt_actual = Δt_measured − (d₂ − d₁) / v
Speed of sound deduced from the same sound dated on two microphones separated by d:
v = d / Δt
where:
- Δt: measured time (s)
- n₁, n₂: sample numbers of the two events
- fₛ: sampling frequency (Hz), typically 44,100 Hz
- δt: resolution, about 2.3 × 10⁻⁵ s at 44.1 kHz
- d, d₁, d₂: source-microphone distances (m)
- v: speed of sound in air, about 340 m·s⁻¹ at 15 °C
Application examples
- Speed of sound over 20 m: the same clap dated on two phones 20.0 m apart gives Δt ≈ 58.8 ms. With a resolution of 23 µs, the clock-related uncertainty is 0.04% - negligible compared with the uncertainty of measuring the 20 m with a tape.
- Falling marble: a marble dropped from 1.00 m hits the floor after t = √(2h/g) = 0.452 s. The acoustic stopwatch separates the click of the release and the impact on the floor, and allows g to be recovered to within a few percent.
- Successive bounces: by dating the impacts of a bouncing ball, you obtain a sequence of durations in geometric progression, with a ratio equal to the coefficient of restitution. A tennis ball typically gives a height ratio of 0.55.
- Echo off a wall: a clap 50 m from a large facade comes back after Δt = 2 × 50 / 340 ≈ 0.29 s, easily measurable.
- Reaction time: comparing the time between a sound cue and a student’s clapped response (about 0.2 s) with the time between two cues produced by the device itself highlights human latency.
- Race timing: in sport, timing the start from the pistol shot uses the same principle, with sensors placed as close as possible to eliminate the propagation delay.
FAQ
Q: Why is the acoustic stopwatch more precise than a handheld stopwatch? A: Because no human reaction is involved. The date of each event is read from the audio recording, sampled 44,100 times per second, giving a resolution of about 23 µs. An operator’s reaction time is of the order of 200 ms, and it fluctuates by several tens of milliseconds from one trial to the next.
Q: Do you have to account for the time the sound takes to reach the mic? A: Yes, as soon as the distance is no longer negligible. Sound travels one meter in 2.9 ms. If the two events happen at the same place, the delay is identical for both and cancels in the difference. If they happen at different places, it must be corrected explicitly.
Q: How do you choose the trigger threshold? A: Above the background noise, but well below the level of the sounds to detect. A good rule of thumb: read the ambient noise level, then set the threshold about 10 dB higher. Also check that an echo does not re-trigger the stopwatch.
Q: Can two different smartphones be used? A: Yes, provided you only compare durations measured on the same device, or synchronize the two with a shared signal at the start of the experiment. The internal clocks of two phones are not aligned, and the absolute offset between them has no physical meaning.
Q: What kind of sound should be produced? A: A short, loud sound with a sharp attack: a hand clap, two metal rulers striking, a balloon popping. A soft or gradual sound crosses the threshold at a poorly defined instant, adding an uncertainty of several milliseconds - far more than the device’s resolution.
Related concepts
Speed of Sound - Sampling - Oscillogram - Echo - Measurement Uncertainty - Free Fall