Wave Speed

Wave speed (celerity) is the propagation velocity of a wave in a given medium, meaning the distance traveled by the disturbance per unit time.

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How to measure it in class

Steps:

Place two smartphones at a known distance (e.g., 10 meters). Open FizziQ on both devices and configure the sound trigger to record.
Produce a brief sound (hand clap) near the first smartphone. Both devices record the sound.
Measure the time delay between the two recordings. This delay corresponds to the time taken by sound to travel the distance separating the two smartphones.
Calculate the speed: v = d/Δt. Compare the obtained value with the theoretical value of 343 m/s at 20°C. Discuss sources of uncertainty.

Scientific activities on this topic

Several experiments easily performed with a smartphone, tablet, or computer allow you to measure wave speed (celerity).

1: Speed of Sound - Measuring the speed of sound with a smartphone: https://www.fizziq.org/en/activities/speed-of-sound/

2: Helmholtz - Measuring the speed of sound through the resonance frequency of a tube: https://www.fizziq.org/en/activities/helmholtz/

3: Tube Effect - Measuring the speed of sound by emitting noise in a tube: https://www.fizziq.org/en/activities/tube-effect/

4: Sound of a Bottle - Measuring the speed of sound by uncorking a wine bottle: https://www.fizziq.org/en/activities/the-sound-of-a-bottle/

Learn more

A bit of history

The first measurements of sound speed date back to the 17th century. In 1636, Marin Mersenne estimated the speed of sound at approximately 450 m/s by measuring the time between a cannon flash and its sound. More precise measurements were obtained in the 19th century through Victor Regnault’s experiments in the Paris sewers.

Speed in different media

Sound travels at 343 m/s in air at 20°C, 1,480 m/s in fresh water, 5,120 m/s in steel, and approximately 6,000 m/s in diamond. However, sound does not propagate in vacuum because it requires a material medium.

The sound barrier

When an aircraft exceeds the speed of sound (Mach 1), it creates a shock wave that produces a sonic boom. Chuck Yeager broke the sound barrier for the first time in 1947 aboard the Bell X-1.

Additional experiments:

The experiment Speed of Sound allows measuring the speed of sound with two smartphones and obtaining a result accurate to within 5%.

Formula

v = λ × f = λ / T

Where:

v: wave speed (m/s)
λ: wavelength (m)
f: frequency (Hz)
T: period (s)

For sound in air: v ≈ 331 + 0.6 × θ (m/s), where θ is temperature in °C.

Application examples

Lightning and thunder: by counting 3 seconds between lightning and thunder, we deduce that the storm is approximately 1 km away
Submarine sonar uses the speed of sound in water (1,500 m/s) to measure depth
Medical ultrasound uses the speed of sound in tissues to build images of the body
The sound barrier corresponds to the moment when an aircraft reaches the speed of sound in air
Musicians in a large orchestra may perceive a slight delay due to the propagation time of sound

FAQ

Q: What is the speed of sound in air? A: Sound travels at approximately 343 m/s in air at 20°C. This speed increases by about 0.6 m/s for each additional degree Celsius.

Q: Why does sound travel faster in water? A: In water, molecules are closer together. The disturbance is therefore transmitted more quickly from one molecule to another. Sound reaches approximately 1,500 m/s in water.

Q: Does wave speed depend on frequency? A: For sound in air, no. All sounds travel at the same speed regardless of their frequency. This is why an orchestra sounds in tune from a distance.

Q: What is the difference between celerity and velocity? A: In wave physics, celerity specifically refers to the propagation speed of the wave. It is distinguished from the velocity of the medium’s particles, which oscillate in place.

Q: How does temperature affect the speed of sound? A: The warmer the air, the more agitated the molecules are and the faster they transmit the disturbance. The speed increases by approximately 0.6 m/s per degree Celsius.

Wavelength - Frequency - Speed of sound - Doppler effect - Propagation medium - Sound barrier - Refraction