485
17-3 INTERFERENCE
ϭ 1.1 ϫ 10
Ϫ5
m ϭ 11 mm.
(Answer)
That is only about one-seventh the thickness of a book page.
Obviously, the displacement amplitude of even the loudest
sound that the ear can tolerate is very small. Temporary exposure to such loud sound produces temporary hearing loss,
probably due to a decrease in blood supply to the inner ear.
Prolonged exposure produces permanent damage.
The pressure amplitude ⌬p m for the faintest detectable
sound at 1000 Hz is 2.8 ϫ 10
Ϫ5
Pa. Proceeding as above
leads to s m ϭ 1.1 ϫ 10
Ϫ11
m or 11 pm, which is about onetenth the radius of a typical atom. The ear is indeed a sensitive detector of sound waves.
s m ϭ
28 Pa
(343 m/s)(1.21 kg/m
3
)(2)(1000 Hz)
Sample Problem 17.01 Pressure amplitude, displacement amplitude
The maximum pressure amplitude p m that the human ear can
tolerate in loud sounds is about 28 Pa (which is very much less
than the normal air pressure of about 10
5
Pa). What is the displacement amplitude s m for such a sound in air of density r ϭ
1.21 kg/m
3
,at a frequency of 1000 Hz and a speed of 343 m/s?
KEY IDEA
The displacement amplitude s m of a sound wave is related to
the pressure amplitude ⌬p m of the wave according to Eq. 17-14.
Calculations: Solving that equation for s m yields
.
Substituting known data then gives us
s m ϭ
⌬p m
v
ϭ
⌬p m
v(2f )
⌬
Additional examples, video, and practice available at WileyPLUS
17-3 INTERFERENCE
Learning Objectives
waves with the same amplitude, wavelength, and travel direction, determine the type of interference between the
waves (fully destructive interference, fully constructive interference, or indeterminate interference).
17.16 Convert a phase difference between radians, degrees,
and number of wavelengths.
● The interference of two sound waves with identical wavelengths passing through a common point depends on their phase
difference f there. If the sound waves were emitted in phase and
are traveling in approximately the same direction, f is given by
where ⌬L is their path length difference.
● Fully constructive interference occurs when f is an integer
multiple of 2p,
f ϭ
⌬L
l
2p,
f m(2p),
for m 0, 1, 2, . . . ,
and, equivalently, when ⌬L is related to wavelength l by
ϭ 0, 1, 2, . . . .
● Fully destructive interference occurs when f is an odd multiple
of p,
f ϭ (2m ϩ 1)p,
for m ϭ 0, 1, 2, . . . ,
ϭ 0.5, 1.5, 2.5, . . . .
⌬L
l
⌬L
l
ϭ
ϭ
After reading this module, you should be able to . . .
17.14 If two waves with the same wavelength begin in
phase but reach a common point by traveling along different paths, calculate their phase difference f at that
point by relating the path length difference ⌬L to the
wavelength l.
17.15 Given the phase difference between two sound
Key Ideas
Interference
Like transverse waves, sound waves can undergo interference. In fact, we can
write equations for the interference as we did in Module 16-5 for transverse
waves. Suppose two sound waves with the same amplitude and wavelength are
traveling in the positive direction of an x axis with a phase difference of f.We can
express the waves in the form of Eqs. 16-47 and 16-48 but, to be consistent with
Eq. 17-12, we use cosine functions instead of sine functions:
s 1 (x, t) ϭ s m cos(kx Ϫ vt)
and
17-3 INTERFERENCE
ϭ 1.1 ϫ 10
Ϫ5
m ϭ 11 mm.
(Answer)
That is only about one-seventh the thickness of a book page.
Obviously, the displacement amplitude of even the loudest
sound that the ear can tolerate is very small. Temporary exposure to such loud sound produces temporary hearing loss,
probably due to a decrease in blood supply to the inner ear.
Prolonged exposure produces permanent damage.
The pressure amplitude ⌬p m for the faintest detectable
sound at 1000 Hz is 2.8 ϫ 10
Ϫ5
Pa. Proceeding as above
leads to s m ϭ 1.1 ϫ 10
Ϫ11
m or 11 pm, which is about onetenth the radius of a typical atom. The ear is indeed a sensitive detector of sound waves.
s m ϭ
28 Pa
(343 m/s)(1.21 kg/m
3
)(2)(1000 Hz)
Sample Problem 17.01 Pressure amplitude, displacement amplitude
The maximum pressure amplitude p m that the human ear can
tolerate in loud sounds is about 28 Pa (which is very much less
than the normal air pressure of about 10
5
Pa). What is the displacement amplitude s m for such a sound in air of density r ϭ
1.21 kg/m
3
,at a frequency of 1000 Hz and a speed of 343 m/s?
KEY IDEA
The displacement amplitude s m of a sound wave is related to
the pressure amplitude ⌬p m of the wave according to Eq. 17-14.
Calculations: Solving that equation for s m yields
.
Substituting known data then gives us
s m ϭ
⌬p m
v
ϭ
⌬p m
v(2f )
⌬
Additional examples, video, and practice available at WileyPLUS
17-3 INTERFERENCE
Learning Objectives
waves with the same amplitude, wavelength, and travel direction, determine the type of interference between the
waves (fully destructive interference, fully constructive interference, or indeterminate interference).
17.16 Convert a phase difference between radians, degrees,
and number of wavelengths.
● The interference of two sound waves with identical wavelengths passing through a common point depends on their phase
difference f there. If the sound waves were emitted in phase and
are traveling in approximately the same direction, f is given by
where ⌬L is their path length difference.
● Fully constructive interference occurs when f is an integer
multiple of 2p,
f ϭ
⌬L
l
2p,
f m(2p),
for m 0, 1, 2, . . . ,
and, equivalently, when ⌬L is related to wavelength l by
ϭ 0, 1, 2, . . . .
● Fully destructive interference occurs when f is an odd multiple
of p,
f ϭ (2m ϩ 1)p,
for m ϭ 0, 1, 2, . . . ,
ϭ 0.5, 1.5, 2.5, . . . .
⌬L
l
⌬L
l
ϭ
ϭ
After reading this module, you should be able to . . .
17.14 If two waves with the same wavelength begin in
phase but reach a common point by traveling along different paths, calculate their phase difference f at that
point by relating the path length difference ⌬L to the
wavelength l.
17.15 Given the phase difference between two sound
Key Ideas
Interference
Like transverse waves, sound waves can undergo interference. In fact, we can
write equations for the interference as we did in Module 16-5 for transverse
waves. Suppose two sound waves with the same amplitude and wavelength are
traveling in the positive direction of an x axis with a phase difference of f.We can
express the waves in the form of Eqs. 16-47 and 16-48 but, to be consistent with
Eq. 17-12, we use cosine functions instead of sine functions:
s 1 (x, t) ϭ s m cos(kx Ϫ vt)
and