The speed of sound is a fundamental physical property representing the distance a sound wave travels through an elastic medium in a given unit of time. While the speed varies significantly depending on the medium, its value in dry air at a standard temperature of 20 degrees Celsius is approximately 343 meters per second. Measuring this speed is a classic physics experiment that demonstrates the relationship between distance, time, and the properties of the transmission medium.
Calculating Speed with the Outdoor Echo Method
The simplest way to calculate the speed of sound involves using an echo and relying on the basic relationship between speed, distance, and time. This technique requires measuring a known distance (d) from a sound source to a large, flat, reflective surface, such as a distant wall or cliff. You will need a reliable measuring tape and a stopwatch or a basic phone timer to record the elapsed time.
Stand a significant distance away from the reflector, ideally 50 meters or more, and measure this distance accurately. Generate a sharp, loud sound, like a hand clap, and record the time (t) from the moment the sound is created until the distinct echo returns to the listener.
Since the sound wave travels to the wall and then back, the total distance traveled is twice the measured distance (2d). The speed of sound (c) is calculated using the formula c = 2d/t. Repeating this measurement multiple times and calculating an average helps to reduce errors caused by human reaction time and inconsistent timing.
Achieving Precision with Smartphone Apps
The precision of the echo method is often limited by the human reaction time involved in starting and stopping a manual stopwatch. Modern smartphones overcome this limitation by acting as highly accurate acoustic sensors. Specialized physics applications or audio recording software utilize the phone’s microphone to record and analyze sound waves with millisecond-level accuracy.
To perform a precise measurement, the device is placed a known distance from a reflective surface, and a sharp sound is recorded. When the audio file is opened in analysis software, the sound wave appears as a distinct waveform with a clear initial peak, followed shortly by a second peak representing the echo. The time difference between the initial sound peak and the echo peak is precisely measured using the software’s timeline cursor.
This digital analysis removes the human element from the timing process, providing a much finer temporal resolution than a human operator. Another technique involves using two synchronized smartphones placed a measured distance apart to record a loud sound. The time difference between when the sound reaches the first phone and when it reaches the second phone is used to calculate the time of flight, which then yields the speed of sound.
Measuring Speed Using Sound Resonance
Another approach to measuring the speed of sound uses wave properties like frequency and wavelength rather than direct distance and time. This method involves creating standing waves within a column of air, typically using a tuning fork of a known frequency (f) and a resonance tube partially filled with water. The tuning fork is struck and held over the open end of the tube, sending a sound wave down the air column.
The air column’s length is adjusted until the sound’s volume suddenly maximizes, a phenomenon called resonance. At this point, the sound wave traveling down the tube and the wave reflecting off the water’s surface interfere to form a standing wave. The first position of maximum loudness, known as the fundamental resonance, occurs when the length of the air column (L) is equal to one-quarter of the sound wave’s wavelength (\(\lambda\)).
By accurately measuring the length L of the air column at this first resonance point, the full wavelength is calculated as \(\lambda = 4L\). The speed of sound (c) is then calculated using the wave equation \(c = f\lambda\), substituting the known frequency and the measured wavelength. This technique offers a highly controlled, laboratory-based measurement.
Environmental Factors That Influence Measurement
The speed of sound is not a fixed universal constant but is dependent on the properties of the medium it travels through. For sound traveling through air, the single most influential factor is the temperature of the gas. A common approximation shows that the speed of sound increases by roughly 0.6 meters per second for every one-degree Celsius rise in temperature.
Other environmental conditions, such as humidity and air pressure, also play a role, though their influence is less pronounced than that of temperature. Higher humidity slightly increases the speed of sound because the lighter water vapor molecules displace heavier air molecules, lowering the overall density of the air.
Conversely, changes in typical atmospheric pressure have a negligible effect on sound speed, as both the pressure and the density of the air change proportionally, largely cancelling out their effect on the wave velocity. For any precise measurement, the air temperature must be recorded and used to calculate the theoretical speed of sound for comparison.