Sound propagation: definition and smartphone experiments

Sound signal propagation is the travel of a pressure wave through a material medium (air, water, solid), from the source to the receiver. Sound needs matter: it does not propagate in a vacuum, and the wave carries energy without carrying matter.

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How to measure it in class

FizziQ records the microphone signal, displays its waveform and its spectrum, and makes it possible to precisely time a sound event. This is what makes measuring the propagation speed accessible.

Steps:

Place two smartphones at a known distance D, measured with a long tape measure, for example 30 to 50 m in a schoolyard
Start the sound recording on both devices at the same moment
Produce a brief, sharp sound next to the first device: two wooden boards clapped together, or a sharp tap on a saucepan
On each recording, locate the arrival time of the clap by zooming in on the wavefront
Calculate v = D / Δt, where Δt is the difference between the two arrival times
Repeat five to ten times and take the average, then compare to 343 m·s⁻¹ at 20 °C

Scientific activities on this topic

The FizziQ app allows you to perform a large number of experiments on the propagation of sound waves. These activities can be found directly in the app in the Activities tab, and also on our website.

Here are 6 activities on the topic of sound wave propagation that can be performed with a smartphone:

Learn more

Sound propagation is a physical phenomenon that plays an essential role in our ability to communicate and perceive the world around us. For a high school student, deepening the understanding of this concept involves examining the acoustic principles and wave properties that allow sound to travel through different media.

Sound is generated by the vibration of objects, which creates sound waves propagating through the surrounding medium, whether air, water or solids. These waves are pressure fluctuations that travel while carrying energy without carrying matter.

Sound waves are characterized by different elements:

Frequency: The frequency of a sound wave, measured in hertz (Hz), determines its pitch. It corresponds to the number of complete cycles (one compression followed by one rarefaction) that occur in one second. High-pitched sounds have high frequencies, while low-pitched sounds have low frequencies.
Wavelength: The wavelength is the distance between two successive corresponding points in a wave cycle, such as two consecutive compressions or rarefactions. It is inversely proportional to frequency: the higher the frequency, the shorter the wavelength.
Amplitude: The amplitude of a sound wave is related to its volume or intensity. It represents the maximum pressure variation from normal atmospheric pressure. A large amplitude means a loud sound, while a small amplitude indicates a soft sound.
Propagation speed: The speed at which a sound wave propagates depends on the medium through which it travels. It is faster in solids than in liquids, and slower in gases. Temperature also influences the speed of sound in air: the warmer the air, the faster sound propagates.
Timbre: Timbre is a characteristic that distinguishes two sounds of the same frequency and amplitude but emitted by different sources. It is determined by the waveform, which itself is influenced by the harmonic frequencies and the vibration modes of the sound source.
Intensity and sound level: Sound intensity I is expressed in W·m⁻² and measures the energy carried per second and per square meter. The sound intensity level L, on the other hand, is expressed in decibels (dB): it is a logarithmic scale built from I. These are two distinct quantities, not to be confused. The plain decibel does not take into account the ear’s sensitivity to different frequencies; it is the A-weighting, written dB(A), that introduces this correction.

The propagation speed of sound varies with the medium: it is approximately 343 m/s in air at 20°C, faster in water, and even faster in solids such as metal or wood. This difference in speed is due to the physical properties of the medium, in particular its density and elasticity. Understanding these variations is crucial for practical applications, such as the acoustic design of concert halls or sound reinforcement.

The phenomena of reflection, refraction and absorption of sound are also important. Reflection is the origin of echoes and is exploited in technologies such as sonar. Sound refraction, which occurs when waves pass from one medium to another while changing speed and direction, is governed by the speed differences between the layers crossed - in the atmosphere, it is essentially the temperature gradients that bend sound rays. Absorption is the process by which sound energy is converted into another form of energy, often heat, which attenuates sound in certain materials.

Human ears play a key role in receiving sound waves, converting them into electrical signals that our brain interprets as sounds. This transformation is made possible by a complex set of internal structures in the ear, which allow distinguishing nuances of frequency and sound intensity.

What does the speed of sound in air really depend on?

This is the point on which people are most often mistaken. The speed of sound in air depends on the nature of the gas and its temperature, and practically not at all on atmospheric pressure. In the range of usual temperatures, it is often written:

v ≈ 331 + 0.6 × θ (in m·s⁻¹, with θ in °C)

that is 331 m·s⁻¹ at 0 °C and 343 m·s⁻¹ at 20 °C. In other words, approximately 0.6 m·s⁻¹ per degree.

Why doesn’t pressure come into it?

Intuition says that “more compressed” air would transmit sound faster. That is wrong, and the reason is instructive. For a gas, v = √(γP/ρ). If air is compressed at constant temperature, the pressure P increases - but the density ρ increases in exactly the same proportion, since P/ρ = rT for an ideal gas. The quotient P/ρ does not change, so neither does v. Substituting, v = √(γrT): only temperature remains.

Practical consequence: sound does not travel faster at sea level than at altitude because of pressure. If it travels faster there, it is only because it is warmer. The same goes for the weather: on a high-pressure day, the speed of sound is not changed by the barometer.

Sound does not propagate in a vacuum

A sound wave is a mechanical wave: it needs a material support whose particles push each other along step by step. Without matter, no propagation. The historical experiment is that of the vacuum bell jar (Hauksbee, Boyle): a ringing bell placed under a jar from which the air is pumped out becomes inaudible, even though it can still be seen vibrating. This is also why the explosions in science fiction films set in space are, physically, silent.

Speed of sound - Seven activities with a smartphone (FizziQ blog) compares seven protocols and their respective precisions | How to see a sound wave shows how to visualize a sound wave with a smartphone.

Formula

Fundamental relation between speed, frequency and wavelength:

v = λ × f

Speed of sound in air as a function of temperature (linear approximation valid between −20 and +40 °C):

v ≈ 331 + 0.6 × θ

Complete expression for an ideal gas:

v = √(γ × r × T)

Distance traveled by sound (time of flight):

d = v × Δt

Distance of an obstacle by echo (round trip):

d = v × Δt / 2

where:

v: propagation speed of sound (m·s⁻¹)
λ: wavelength (m)
f: frequency (Hz)
θ: temperature in degrees Celsius (°C)
T: absolute temperature (K), T = θ + 273.15
γ: adiabatic coefficient, approximately 1.40 for air
r: specific gas constant of air, approximately 287 J·kg⁻¹·K⁻¹
Δt: propagation time (s)

Application examples

Typical propagation speeds: approximately 343 m·s⁻¹ in air at 20 °C, 1,500 m·s⁻¹ in seawater, 3,200 m·s⁻¹ in wood, 5,000 m·s⁻¹ in steel. Sound therefore travels about 15 times faster in steel than in air.
The thunderstorm rule: the light of the lightning arrives almost instantly, the thunder at 343 m·s⁻¹. Three seconds of delay correspond to approximately 1 km - hence the counting rule “3 seconds = 1 kilometer”.
A 440 Hz sound (the A of a tuning fork) has a wavelength in air of λ = 343 / 440 ≈ 0.78 m. At 20 Hz, it reaches 17 m; at 20 kHz, only 1.7 cm. This factor of a thousand explains why low frequencies bend around obstacles and high frequencies do not.
Medical ultrasound imaging uses ultrasound around 3 to 10 MHz: in tissues (approximately 1,540 m·s⁻¹), the wavelength is less than a millimeter, which sets the fineness of the visible details.
Sonar measures depth by echo: a round trip of 0.2 s in water corresponds to a depth of 1,500 × 0.2 / 2 = 150 m.
The design of concert halls relies on controlling reflections: beyond approximately 50 ms of delay between the direct sound and the reflected sound, the ear separates them and a disturbing echo is perceived.

FAQ

Q: Does sound propagate in a vacuum? A: No. A sound wave is a mechanical wave: it needs a material medium whose particles oscillate step by step. In the vacuum of space, there is nothing to make vibrate. Light, on the other hand, is an electromagnetic wave and needs no support.

Q: Does sound travel faster when atmospheric pressure is higher? A: No, this is a stubborn misconception. At a given composition and temperature, the speed of sound in air depends practically not at all on pressure: when air is compressed, pressure and density increase together and their ratio remains constant. Only temperature really matters.

Q: Do air molecules travel from the source to my ear? A: No. Each molecule oscillates around its equilibrium position over a tiny distance. It is the pressure disturbance - therefore the energy - that propagates, not the matter. It is the same difference as between a wave and the seawater, which stays in place.

Q: Why can you hear the bass of a party through a wall, but not the voices? A: Because the wavelength of low frequencies (several meters) is large compared to obstacles and openings: low frequencies diffract and pass through walls much more easily. High frequencies, with centimeter-scale wavelengths, are reflected and absorbed by the wall.

Q: Why do my two measurements of the speed of sound give very different results? A: Most often, it is not the microphone but the time measurement. Over a short distance, Δt is very small and the slightest imprecision becomes enormous in percentage terms. You need to lengthen the distance (30 m or more), repeat the measurement and average, and check the synchronization of the two devices.

Speed of Sound - Wavelength - Frequency - Echo - Sound Intensity - Doppler Effect - Resonance Frequency

Sound Signal Propagation