Acoustic properties · Stress and velocity
Characteristic acoustic impedance
Does material impedance equal the impedance felt by a string?
Characteristic impedance ρc is a local wave property. Mechanical input impedance of a bridge is a frequency-dependent response of the assembled structure.
Try the interactive demoStart with something familiar
A pulse meeting a different material can partly return and partly continue. The contrast between the two media helps set that split. Material impedance describes this kind of wave relationship, not whether wood is simply “good” or “bad”.
Z₂ = Z₁
No reflection in the ideal model
Z₂ ≠ Z₁
Part reflected, part transmitted
Notice what changes
A travelling wave has stress and particle velocity. Their ratio, in the specified axial model, gives Z = ρc. A material value must name the direction and wave type.
Understand why
For the ideal same-area interface, equal Z gives no reflection. A mismatch produces reflection; its sign indicates the reflected stress phase, not negative energy.
Connect it to wood and making
The assembled violin has geometry, joints and resonances. The impedance seen by a string at the bridge is force divided by velocity and changes with frequency. It is not this scalar material Z.
Put names to the ideas
Stress over particle velocity
For a single travelling axial wave in the slender-rod idealization, the magnitude of stress divided by particle velocity is ρc. SI units are kg/(m²·s), also called Rayl.
Interfaces and reflection
An impedance contrast helps explain wave reflection in simple one-dimensional models. Actual joints introduce geometry, contact and several wave types, so a scalar material ratio cannot describe an entire instrument connection.
Bridge impedance is different
Mechanical input impedance is force divided by velocity at a specified point and direction, with units N·s/m. The inverse is mobility or admittance, and both vary through structural resonances.
In Z = ρc, density and wave speed multiply. In Z_in = F/v, force and velocity describe the assembled structure at a point. The two quantities even have different units.
A worked example
With ρ = 400 kg/m³ and c = 5000 m/s, Z = 2,000,000 Rayl = 2 MRayl. This number cannot be placed on a bridge-admittance chart without a structural model.
Explore it yourself
Read material Z in MRayl for convenience, but retain SI values for calculations. State position and direction when measuring a bridge response.
First, explore the linked metrics
- c
- 5345 m/s
- E′/ρ
- 28.57 10⁶ m²/s²
- R
- 12.73 m⁴/(kg·s)
- Z
- 2.24 MRayl
- Q ≈ 1/η
- 100.0
- ACE
- 1273 m⁴/(kg·s)
E′ + ρ → c → R, Z η → Q → ACE
Then explore an ideal interface
- Stress reflection coefficient
- 0.333
- Reflected energy
- 11.1 %
- Transmitted energy
- 88.9 %