Acoustics · Wave propagation
Longitudinal wave speed
Over the same distance, which pulse arrives first?
Compare longitudinal pulses in two equal-length materials and see how wave speed changes their first-arrival times.
Try the interactive demoStart with something familiar
Think of a row of people passing a brief push down the line. The disturbance can arrive at the far end while each person moves only a little. A wave travels; the material does not have to travel with it.
c = 5000 m/s
L = 1 m · t = 0.20 ms
c = 2500 m/s
L = 1 m · t = 0.40 ms
Notice what changes
Separate local motion from travel. For a longitudinal wave, tiny back-and-forth particle motion is aligned with the direction the disturbance travels.
Understand why
With equal distance, a faster wave arrives earlier. With equal speed, a longer path takes longer. Transit time tells us about propagation, not directly about a vibration’s pitch.
Connect it to wood and making
In the axial rod approximation, elasticity resists compression while density supplies inertia. Their ratio sets the wave-speed scale. Bending and the assembled violin add geometry and different wave behaviour.
Put names to the ideas
Distance, speed and time
Travel time is t = L/c. With distance L fixed, doubling wave speed c halves the travel time. This compares propagation, not ring duration.
The disturbance travels
In a longitudinal wave, particles oscillate locally along the direction of propagation. They do not travel from one end to the other with the pulse.
Longitudinal and bending waves
Longitudinal speed describes axial stretching and compression. Bending waves also depend on thickness, frequency and direction; the two speeds are different quantities.
t = L/c says “time equals distance divided by speed.” In c = √(E′/ρ), increasing E′ at fixed density raises speed; increasing density at fixed E′ lowers it.
A worked example
Over 1 m, a 5000 m/s pulse takes 0.20 ms while a 2500 m/s pulse takes 0.40 ms. The animation is slowed and the particle displacement exaggerated so the travel can be inspected.
Explore it yourself
Change A’s wave speed, compare the arrival times, then use equal speed or replay to observe both pulses starting together.