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Unformatted text preview: 7 (27) At the moment shown in Figure 4, the string element Δl is moving in an arc of a circle. Thus, it has a
centripetal acceleration toward the center of that circle given by (28)
Equations (26)-(28) contain elements of Newton’s second law. Combining them in the form (29)
∆ ∆ (30) Solving equation (30) for the speed v yields (31)
Equation (31) tells us: The speed of a wave along a stretched ideal string depends only on the tension and linear
density of the string and NOT on the frequency of the wave.
The frequency of a wave is fixed entirely by whatever generates the wave. The wavelength of the wave is
then fixed by equation (23) in the form λ=v/f.
2.9 Sound Waves
We saw in the previous sections, mechanical waves are waves that require a material medium to
exist. There are two types of mechanical waves: Transverse waves involve oscillations perpendicular to
the direction in which the waves travels; longitudinal waves involve oscillations parallel to the direction
of wave travel.
For the purpose of this lab, a sound wave is defined roughly as any longitudinal wave. Seismic
prospecting teams use such waves to prove Earth’s crust contains oil. Ships carry sound-ranging gear
(sonar) to detect underwater obstacles. Submarines use sound waves to stalk other submarines, largely by
listening for the characteristic noises produced by the
Figure 5 illustrates several ideas that we shall use in
our discussions. Point S represents a tiny sound source, called
a point source that emits sound waves in all directions. The
wavefronts and rays indicate the direction of travel and the
spread of the sound waves. Wavefronts are surfaces over
which the oscillations due to the sound wave have the same
value; such surfaces are represented by whole or partial
circles in a two-dimensional drawing for a point source. Rays
are directed lines perpendicular to the wavefronts that indicate
the direction of travel of the wavefronts. The short double Figure 5 A sound wave travels from a point S
arrows superimposed on the rays of Figure 5 indicate that the through a three-dimensional medium. Picture
from Fundamentals of Physics 7th edition Wiley
longitudinal oscillations of the air are parallel to the rays.
Near a point source like that of Figure 5, the
wavefronts are spherical and spread out in three-dimensions, and there the waves are said to the spherical. 8 As the wavefronts move outward and their radii become larger, their curvature decreases. Far from the
source, we approximate the wavefronts are planes (or lines on two-dimensional drawings), and the waves
are said to be plan...
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- Fall '09