8.1 Basic Concepts and Formulae
341
Waves in Solids
In solids, compressional and shearing forces are readily transmitted.
(i) Transverse waves in wires/strings in which the elastic properties of the material
are disregarded:
v =
F/μ
(8.4)
(ii) Transverse waves in bars/wires
V ∝
1
λ
Y/ρ
(8.10)
where Y is Young’s modulus of elasticity.
(iii) Longitudinal waves in wires and bars
V =
Y/ρ
(8.11)
(iv) Torsional vibrations in wires/bars
V =
η/ρ
(8.12)
where η is the shear modulus of elasticity.
In all these cases the material of restricted dimension is considered.
Waves in Liquids
The wave motion through liquids is influenced by the gravity and the characteristics
of the medium such as the depth and surface tension.
Canal Waves
If the wavelength is large compared with the wave amplitude, surface tension effect
is small. The controlling factors are then basically gravity (g) and the boundary conditions. Furthermore, if the surface is sufficiently extensive so that the wall effects
are negligible then the depth (h) alone is the main boundary condition. The velocity
(v) of the canal waves is given by
V =
gh
(8.13)
Surface Waves
These are the waves found on relatively deep water. The velocity of deep water
waves is given by
V =
gλ/2π
(8.14)
341
Waves in Solids
In solids, compressional and shearing forces are readily transmitted.
(i) Transverse waves in wires/strings in which the elastic properties of the material
are disregarded:
v =
F/μ
(8.4)
(ii) Transverse waves in bars/wires
V ∝
1
λ
Y/ρ
(8.10)
where Y is Young’s modulus of elasticity.
(iii) Longitudinal waves in wires and bars
V =
Y/ρ
(8.11)
(iv) Torsional vibrations in wires/bars
V =
η/ρ
(8.12)
where η is the shear modulus of elasticity.
In all these cases the material of restricted dimension is considered.
Waves in Liquids
The wave motion through liquids is influenced by the gravity and the characteristics
of the medium such as the depth and surface tension.
Canal Waves
If the wavelength is large compared with the wave amplitude, surface tension effect
is small. The controlling factors are then basically gravity (g) and the boundary conditions. Furthermore, if the surface is sufficiently extensive so that the wall effects
are negligible then the depth (h) alone is the main boundary condition. The velocity
(v) of the canal waves is given by
V =
gh
(8.13)
Surface Waves
These are the waves found on relatively deep water. The velocity of deep water
waves is given by
V =
gλ/2π
(8.14)