14.3 Classical Waves 639
xyz%z*xFigure 14.9 The Electric and Magnetic Fields in an Electromagnetic Wave.visible light, infrared radiation, ultraviolet radiation, X-rays, radio waves, microwaves,
and so on, which differ from each other only in having different wavelengths and
frequencies.
Electromagnetic radiation obeys wave equations similar to other wave equations
except that there are two oscillating quantities, the electric fieldEEEand the magnetic
fieldH. The equations are introduced briefly in Appendix F. These equations lead
to standing waves and traveling waves similar to waves in a string. The electric field
cannot oscillate without the magnetic field and vice versa, so the electromagnetic wave
behaves like a single wave. Figure 14.9 depicts a plane polarized wave traveling in the
ydirection, with the electric fieldEEEoscillating in thezdirection and with the magnetic
fieldH oscillating in thexdirection. As time passes, this traveling wave moves to
the right without changing its shape or wavelength. Appendix F contains additional
information about electromagnetic waves.
It was originally thought that all space was filled by a substance called the “lumi-
niferous ether,” which was supposedly the medium that oscillated when electromag-
netic waves propagated. This medium would have to be very rigid for the speed of light
to be as large as it is, but it could not impede the motions of objects moving through it.
The existence of such a medium was disproved when Michelson and Morley found that
the speed of light was independent of the motion of the observer. This experimental
fact was the origin of Einstein’s special theory of relativity, and we now know that
electromagnetic waves do not require a material medium in which to oscillate.Albert Abraham Michelson, 1852–1931,
a German-American physicist, and
Edward Morley, 1838–1923, an
American chemist, collaborated on
these measurements in 1887 at Case
Western Reserve University.
Electric and magnetic fields exert forces on charged particles so that molecules and
atoms can absorb electromagnetic radiation. The converse is also true. According to
Maxwell’s theory, oscillating electric charges emit electromagnetic radiation.PROBLEMS
Section 14.3: Classical Waves
14.9 If a violin string has a fundamental frequency of 264 s−^1 ,
find the frequency of each of the first three overtones.
14.10The speed of sound in air at 25◦C is 346.2 m s−^1. Find
the wavelength of the sound wave with frequency
264 s−^1 at this temperature.14.11 a.In a closed organ pipe, the wavelength of the
fundamental wave corresponds to twice the length of
the pipe. Find the length of the pipe that is needed at
25 ◦C for “A” above “middle C,” which has frequency
equal to 440 s−^1. Assume that the speed of sound in
air is 346.2 m s−^1 at 25◦C. What do you think will
happen to the pitch if the temperature increases?