Asked by zoie
Why do mechanical waves travel fastest in solids? (think of people standing close together they can send a message faster than if they are far apart)
The close particles transfer the energy faster.
The close particles transfer the energy slower.
All Answers 1
Answered by
GPT-5 mini
AI
The correct choice is: The close particles transfer the energy faster.
Why: the speed of a mechanical wave depends on how quickly a disturbance on one particle produces a restoring force that moves the next particle. In continuum form this is set by the material’s stiffness (elastic modulus or bulk modulus) divided by its density. For example:
- longitudinal waves in a rod: v = sqrt(E/ρ)
- sound in a fluid: v = sqrt(B/ρ)
Solids have particles much closer together and much stronger interparticle (bond) forces than gases or liquids, so their elastic modulus (E or B) is very large. Even though solids can be denser, the large stiffness typically wins, so v is much larger in solids. Intuitively: if people stand close and are tightly linked, a shove is transmitted quickly to the neighbor; if they are far apart or weakly linked, the shove takes longer to reach the next person.
So the key is not just “closeness” alone but the strength of coupling (stiffness) and the mass per volume (density). Closely spaced, strongly coupled particles transmit disturbances faster.
Why: the speed of a mechanical wave depends on how quickly a disturbance on one particle produces a restoring force that moves the next particle. In continuum form this is set by the material’s stiffness (elastic modulus or bulk modulus) divided by its density. For example:
- longitudinal waves in a rod: v = sqrt(E/ρ)
- sound in a fluid: v = sqrt(B/ρ)
Solids have particles much closer together and much stronger interparticle (bond) forces than gases or liquids, so their elastic modulus (E or B) is very large. Even though solids can be denser, the large stiffness typically wins, so v is much larger in solids. Intuitively: if people stand close and are tightly linked, a shove is transmitted quickly to the neighbor; if they are far apart or weakly linked, the shove takes longer to reach the next person.
So the key is not just “closeness” alone but the strength of coupling (stiffness) and the mass per volume (density). Closely spaced, strongly coupled particles transmit disturbances faster.
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