Acoustic properties · Dissipation
Loss factor and internal friction
Where does the energy go after a tap?
Loss factor describes the dissipative part of a material’s dynamic response. It supplies information that density and elastic modulus alone cannot provide.
Try the interactive demoStart with something familiar
A playground swing gradually slows even after you stop pushing. Some mechanical energy becomes heat or leaves through the surroundings. Wood vibrations also lose energy, though the loss mechanisms are more varied.
Amplitude in time
f = 500 Hz · Q = 50 / 150
Peak width
Green: Q = 50 · Blue: Q = 150
Notice what changes
Elastic storage is the recoverable part of deformation. Loss describes the portion not returned as mechanical vibration in each cycle; it is not the same quantity as mass or stiffness.
Understand why
At the same mode frequency and initial amplitude, greater loss leads to faster decay. Compare equal conditions: a quiet initial tap can disappear sooner simply because it began closer to noise.
Connect it to wood and making
A held blank also loses energy into the fingers or support. Separate material behaviour from the test arrangement before connecting a measured decay to wood selection.
Put names to the ideas
Storage and loss
For linear harmonic response, tan δ = E″/E′. Here η denotes that loss factor; notation varies, so define it rather than confusing it with a viscous coefficient in N·s/m.
An independent measurement
Two samples can share density and modulus yet have different decay. A damping measurement is required; deriving c, R and Z from the elastic quantities does not reveal η.
Measured loss includes the setup
Support contact, radiation, room contamination and recording processing can alter an observed decay. Reproducible specimen conditions are needed before attributing all measured loss to the material.
η or tan δ compares the loss part with the storage part in a harmonic test. For weak damping, Q is approximately its reciprocal: more loss means smaller Q.
A worked example
In a lightly damped, isolated mode, η = 0.01 corresponds approximately to Q = 100. Halving η doubles Q, but decay time also depends on frequency.
Explore it yourself
Compare decay at the same frequency or state the frequency explicitly. Keep damping measured rather than inferred from a material grade.
- τA
- 63.7 ms
- Δf (−3 dB)
- 5.00 Hz
- T60
- 0.44 s