638
14 Classical Mechanics and the Old Quantum Theory
so that νt ct/λ, or
ν
c
λ
(14.3-34)
Equation (14.3-34) is the general relation between wavelength and frequency for a
traveling wave. This important equation holds for all kinds of waves, including sound
waves and electromagnetic waves. If we replace λ by 2L/n and c by
T /ρ we obtain
ν
n
2L
T
ρ
(14.3-35)
which is identical to Eq. (14.3-23), the formula for the frequency of a standing wave.
Using Eqs. (14.3-30) and (14.3-34), we can now write
z(x, t) Asin
2πx
λ
− 2πνt
(14.3-36)
Exercise 14.11
In addition to waves in strings, other oscillations such as sound waves obey wave equations.
The speed of sound in air at sea level and 20 ◦ C is 343 m s −1 . Find the wavelength of a sound
wave with a frequency of 440 s −1 , or 440 Hertz. (This frequency is the frequency of “A” above
middle “C” in the musical scale.)
Two traveling waves moving in opposite directions can interfere to produce a standing
wave. The two traveling waves
z R (x, t) Asin(κx − κct)
(14.3-37a)
and
z L (x, t) Asin(κx + κct)
(14.3-37b)
interfere to give
z(x, t) z R (x, t) + z L (x, t) A[sin(κx + κct) + sin(κx − κct)]
(14.3-38)
which by the use of trigonometric identities is the same as the standing wave
z(x, t) 2Asin(κx) cos(κct)
(14.3-39)
Exercise 14.12
Use trigonometric identities to obtain Eq. (14.3-39) from Eq. (14.3-38).
The Wave Theory of Electromagnetic Radiation
James Clerk Maxwell, 1831–1879, was
a British physicist who made
fundamental contributions to
electrodynamics, gas kinetic theory, and
thermodynamics.
In 1865, Maxwell developed a mathematical theory of electromagnetism. According
to this theory the electric field E E E and the magnetic field H can oscillate like waves,
constituting electromagnetic radiation. Examples of electromagnetic radiation are
14 Classical Mechanics and the Old Quantum Theory
so that νt ct/λ, or
ν
c
λ
(14.3-34)
Equation (14.3-34) is the general relation between wavelength and frequency for a
traveling wave. This important equation holds for all kinds of waves, including sound
waves and electromagnetic waves. If we replace λ by 2L/n and c by
T /ρ we obtain
ν
n
2L
T
ρ
(14.3-35)
which is identical to Eq. (14.3-23), the formula for the frequency of a standing wave.
Using Eqs. (14.3-30) and (14.3-34), we can now write
z(x, t) Asin
2πx
λ
− 2πνt
(14.3-36)
Exercise 14.11
In addition to waves in strings, other oscillations such as sound waves obey wave equations.
The speed of sound in air at sea level and 20 ◦ C is 343 m s −1 . Find the wavelength of a sound
wave with a frequency of 440 s −1 , or 440 Hertz. (This frequency is the frequency of “A” above
middle “C” in the musical scale.)
Two traveling waves moving in opposite directions can interfere to produce a standing
wave. The two traveling waves
z R (x, t) Asin(κx − κct)
(14.3-37a)
and
z L (x, t) Asin(κx + κct)
(14.3-37b)
interfere to give
z(x, t) z R (x, t) + z L (x, t) A[sin(κx + κct) + sin(κx − κct)]
(14.3-38)
which by the use of trigonometric identities is the same as the standing wave
z(x, t) 2Asin(κx) cos(κct)
(14.3-39)
Exercise 14.12
Use trigonometric identities to obtain Eq. (14.3-39) from Eq. (14.3-38).
The Wave Theory of Electromagnetic Radiation
James Clerk Maxwell, 1831–1879, was
a British physicist who made
fundamental contributions to
electrodynamics, gas kinetic theory, and
thermodynamics.
In 1865, Maxwell developed a mathematical theory of electromagnetism. According
to this theory the electric field E E E and the magnetic field H can oscillate like waves,
constituting electromagnetic radiation. Examples of electromagnetic radiation are