Speed of sound
This activity allows students to measure the speed of sound using two synchronized acoustic stopwatches. It reproduces a historic scientific experiment with modern tools.
In 1635, French philosopher Marin Mersenne became the first person to measure the speed of sound with reasonable accuracy. His method was elegant: he observed a cannon being fired from a distant hill, measured the time delay between seeing the flash and hearing the bang, and divided the known distance by the elapsed time. His result, approximately 316 m/s, was remarkably close to the modern accepted value of 343 m/s at 20°C. Today, we can reproduce this fundamental measurement with far greater precision using digital tools. FizziQ's acoustic stopwatch, which starts and stops automatically when it detects a sound exceeding a threshold, eliminates human reaction time from the measurement. By placing two smartphones a known distance apart and triggering both with the same pair of sounds (hand claps), the difference in recorded times reveals the sound travel time over that distance, yielding a direct measurement of the speed of sound.
Learning objectives:
The student uses two smartphones equipped with the FizziQ sound stopwatch to determine the time it takes for the sound to travel a known distance. After programming both devices to start and stop at the same sound signals the student separates them by a measured distance and then calculates the speed of the sound from the difference between the recorded times divided by the distance.
Level:
High school
FizziQ
Author:
Duration (minutes) :
30
What students will do :
- Measure the speed of sound using two acoustic stopwatches separated by a known distance
- Understand the principle of differential timing to eliminate systematic errors
- Compare the measured speed with the accepted value and evaluate sources of error
- Investigate the effect of temperature on the speed of sound
- Connect the experiment to the historical measurements of the speed of sound
Scientific concepts:
- Sound propagation
- Speed of sound waves
- Differential timing
- History of science
- Metrology
Sensors:
- Microphone (acoustic trigger / sound stopwatch on both phones)
What is required:
- Two smartphones with the FizziQ application
- A clear space of at least 5 meters
- A tape measure to measure distance
- FizziQ experience notebook
Experimental procedure:
Open FizziQ on both smartphones and set up the acoustic stopwatch (sound-triggered timer) on each.
Calibrate the sound threshold on both phones so they trigger reliably on a hand clap but not on background noise.
Place the two smartphones on the same table, side by side. Perform a test: clap once to start both, then clap again to stop both. The recorded times should be nearly identical (within a few milliseconds).
Now separate the smartphones by a measured distance. Start with 5 meters between them, measured precisely with a tape measure.
Stand at one end (near Phone A). Clap once to start both stopwatches. Both phones should start simultaneously (sound reaches both within ~15 ms at 5 m).
Wait 3-5 seconds, then clap again near Phone A to stop both. Phone A stops instantly; Phone B stops after a slight delay (the time for the second clap to travel 5 meters).
Record the time displayed on each phone: T_A and T_B. The difference ΔT = T_B - T_A is the sound travel time over the 5-meter distance.
Calculate the speed of sound: v = distance / ΔT.
Repeat the measurement 5 times and calculate the average and standard deviation.
Increase the distance to 10 meters and repeat. A longer distance gives a larger ΔT, reducing relative error.
Try distances of 15 and 20 meters if the space permits. Plot speed versus distance to check consistency.
Compare your result with the theoretical speed at the current air temperature: v = 331.3 + 0.606 × T(°C) m/s.
Expected results:
The measured speed of sound should fall between 330 and 360 m/s, depending on temperature (the accepted value is 343 m/s at 20°C, increasing by about 0.6 m/s per degree Celsius). At 5 meters, the time difference ΔT is only about 14.6 ms, which requires precise acoustic triggering to measure. At 10-20 meters, the time difference increases to 29-58 ms, giving more reliable results. The standard deviation across repeated measurements is typically 5-15% at 5 meters but improves to 3-8% at 10+ meters. Wind can introduce systematic errors if it consistently blows along or against the direction of sound propagation. The main source of random error is the acoustic trigger precision (±1-2 ms).
Scientific questions:
- Why does the differential timing method (using two phones) eliminate the reaction time error?
- How does temperature affect the speed of sound? Why?
- Why does a longer measurement distance generally give a more precise result?
- How did Marin Mersenne measure the speed of sound in 1635, and how accurate was his result?
- What is the speed of sound in water? In steel? Why are these so different from air?
- How is the speed of sound related to the properties of the medium (density, elasticity)?
Scientific explanations:
Measuring the speed of sound has fascinated scientists for centuries. In 1635, Marin Mersenne was the first to determine a reasonably precise value (around 316 m/s) by measuring the time elapsed between the observation of a cannon flash and the perception of the associated sound.
This modern experiment reproduces this principle but with much greater precision thanks to digital technology. FizziQ's sound timer automatically triggers when sound amplitude exceeds a certain threshold, eliminating errors due to human reaction time.
Both timers start simultaneously with the first clap, but stop at slightly different times during the second clap: the timer near the source stops immediately, while the one further away records a longer time, precisely corresponding to the sound propagation delay. This delay Δt, compared to the distance d between the two devices, makes it possible to directly calculate the speed of sound: v = d/Δt.
Theoretically, the speed of sound in air depends mainly on temperature according to the formula: v = 331.3 + 0.606×T (m/s), where T is the temperature in °C. At 20°C, this speed is approximately 343 m/s.
The accuracy of this experiment depends on several factors: 1) The accuracy of the distance measurement; 2) The sensitivity of the microphones and the consistency of their trigger thresholds; 3) The absence of parasitic sound reflections; 4) Atmospheric conditions (temperature, humidity, pressure). By carrying out several measurements and calculating their average, we can achieve an accuracy of around 1-2%, much better than that obtained by Mersenne.
This experiment illustrates not only a fundamental physical phenomenon, but also the evolution of scientific methods: the principle has remained the same for four centuries, but the precision has considerably improved thanks to technological advances.
Extension activities:
- Why does the differential timing method (using two phones) eliminate the reaction time error?
- How does temperature affect the speed of sound? Why?
- Why does a longer measurement distance generally give a more precise result?
- How did Marin Mersenne measure the speed of sound in 1635, and how accurate was his result?
- What is the speed of sound in water? In steel? Why are these so different from air?
- How is the speed of sound related to the properties of the medium (density, elasticity)?
Frequently asked questions:
Q: The time difference between the two phones is sometimes negative or zero. What went wrong?
R: The first clap must reach both phones nearly simultaneously (they should be close to you), and the second clap must travel a significant distance. If you accidentally stand closer to Phone B for the second clap, the time difference can be reversed. Always perform the second clap right next to Phone A.
Q: My calculated speed of sound is much higher or lower than 343 m/s. What are the likely causes?
R: The most common error is in the distance measurement or the acoustic trigger timing. At 5 meters, even a 2 ms trigger error translates to ±50 m/s. Use the longest distance practical and average multiple measurements.
Q: Does the method work if there is wind?
R: Wind adds or subtracts from the sound speed depending on direction. A 10 km/h wind can change the effective speed by about ±3 m/s. For the most accurate results, measure on a calm day or average measurements in both directions.
Q: Can I use this method indoors?
R: Yes, but reflections from walls can cause the acoustic trigger to fire on echoes rather than the direct sound. Use a large room and position the phones away from walls. The first trigger event is the most reliable.