`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 me-

dium 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 = —pv 2 (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 pro-

pagation 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/m 2. 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 = 14 7- 8 01-Lo. (4.4a) - In a travelling electromagnetic wave:

theeo = (4.4b) - Space density of the energy of an electromagnetic field:

`w= +`

`ED BH`

2 2 • (4.4c)

- Flow density of electromagnetic energy, the Poynting vector:

S = [EH]. (4.4d) - Energy flow density of electric dipole radiation in a far field zone:

`S •-•-• - r sin`

(^1 2) - , v, (4.4e)

2

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