4.184. An observer A located at a distance rA —5,0 m from a
ringing tuning fork notes the sound to fade away T = 19 s later
than an observer B who is located at a distance r = 50 m from
the tuning fork. Find the damping coefficient 13 of `Oscillations of
the tuning fork. The sound velocity v = 340 m/s.
4.185. A plane longitudinal harmonic wave propagates in a medium with density p. The velocity of the wave propagation is v.
Assuming that the density variations of the medium, induced by the
propagating wave, Ap < p, demonstrate that
(a) the pressure increment in the medium Ap = —pv2 (n/ax),
where aVax is the relative deformation;
(b) the wave intensity is defined by Eq. (4.3i).
4.186. A ball of radius R = 50 cm is located in the way of propagation of a plane sound wave. The sonic wavelength is = 20 cm,
the frequency is v = 1700 Hz, the pressure oscillation amplitude
in air is (Ap)„, = 3.5 Pa. Find the mean energy flow, averaged over
an oscillation period, reaching the surface of the ball.
4.187. A point A is located at a distance r = 1.5 m from a point
isotropic source of sound of frequency v = 600 Hz. The sonic power
of the source is P = 0.80 W. Neglecting the damping of the waves
and assuming the velocity of sound in air to be equal to v = 340 m/s,
find at the point A:
(a) the pressure oscillation amplitude (Ap),„, and its ratio to the
air pressure;
(b) the oscillation amplitude of particles of the medium; compare
it with the wavelength of sound.
4.188. At a distance r = 100 m from a point isotropic source of
sound of frequency 200 Hz the loudness level is equal to L = 50 dB.
The audibility threshold at this frequency corresponds to the sound
intensity / 0 = 0.10 nW/m2. The damping coefficient of the sound
wave is Y = 5.0.10-4 m-1. Find the sonic power of the source.
4.4. ELECTROMAGNETIC WAVES, RADIATION
• Phase velocity of an electromagnetic wave:
v = c/1/eµ, where c = 1 47- 801-Lo.
(4.4a)
• In a travelling electromagnetic wave:
theeo =
(4.4b)
• Space density of the energy of an electromagnetic field:
w= +
ED BH
(4.4c)
2 2 •
• Flow density of electromagnetic energy, the Poynting vector:
S = [EH].
(4.4d)
• Energy flow density of electric dipole radiation in a far field zone:
r
S •-•-• - sin
2
-
,
v,
(4.4e)
1
2
13-9451
ringing tuning fork notes the sound to fade away T = 19 s later
than an observer B who is located at a distance r = 50 m from
the tuning fork. Find the damping coefficient 13 of `Oscillations of
the tuning fork. The sound velocity v = 340 m/s.
4.185. A plane longitudinal harmonic wave propagates in a medium with density p. The velocity of the wave propagation is v.
Assuming that the density variations of the medium, induced by the
propagating wave, Ap < p, demonstrate that
(a) the pressure increment in the medium Ap = —pv2 (n/ax),
where aVax is the relative deformation;
(b) the wave intensity is defined by Eq. (4.3i).
4.186. A ball of radius R = 50 cm is located in the way of propagation of a plane sound wave. The sonic wavelength is = 20 cm,
the frequency is v = 1700 Hz, the pressure oscillation amplitude
in air is (Ap)„, = 3.5 Pa. Find the mean energy flow, averaged over
an oscillation period, reaching the surface of the ball.
4.187. A point A is located at a distance r = 1.5 m from a point
isotropic source of sound of frequency v = 600 Hz. The sonic power
of the source is P = 0.80 W. Neglecting the damping of the waves
and assuming the velocity of sound in air to be equal to v = 340 m/s,
find at the point A:
(a) the pressure oscillation amplitude (Ap),„, and its ratio to the
air pressure;
(b) the oscillation amplitude of particles of the medium; compare
it with the wavelength of sound.
4.188. At a distance r = 100 m from a point isotropic source of
sound of frequency 200 Hz the loudness level is equal to L = 50 dB.
The audibility threshold at this frequency corresponds to the sound
intensity / 0 = 0.10 nW/m2. The damping coefficient of the sound
wave is Y = 5.0.10-4 m-1. Find the sonic power of the source.
4.4. ELECTROMAGNETIC WAVES, RADIATION
• Phase velocity of an electromagnetic wave:
v = c/1/eµ, where c = 1 47- 801-Lo.
(4.4a)
• In a travelling electromagnetic wave:
theeo =
(4.4b)
• Space density of the energy of an electromagnetic field:
w= +
ED BH
(4.4c)
2 2 •
• Flow density of electromagnetic energy, the Poynting vector:
S = [EH].
(4.4d)
• Energy flow density of electric dipole radiation in a far field zone:
r
S •-•-• - sin
2
-
,
v,
(4.4e)
1
2
13-9451