3. SIMILARITIES IN PROPAGATION OF LIGHT AND SOUND WAVES
 
   The speed of light is extremely high, and for a long time there was a theory that light could instantaneously reach the most distant points; in a word, it was considered that the speed of light is infinite. Galileo was the first who tried to find it experimentally, but without success. The first person who succeeded in approximately determining the speed of light, by observing the eclipse of the first satellite of Jupiter in 1675, was Olaf Römer.
   Because of the high speed of light, it is difficult to follow, examine, and therefore understand all phenomena connected to its behavior. Light's motion is wavelike in nature as is sound. These two natural phenomena have a lot in common, for example: propagation (plane and spherical wave), interference, the Doppler effect, refraction, reflection etc. The speed of sound in the air is about 9·10⁵ times lower than the speed of light. That is why it is much easier to perceive, follow and measure certain phenomena present in sound rather than in light. Therefore, in order to understand with ease some phenomena connected with the light and treated by the theory of special relativity it should, at first, to consider the propagation of sound in the air, and to compare it with the propagation of light in a vacuum.
   Let us assume that at a point in the homogeneous air environment there is a sinusoidal oscillator whose oscillation generates a spherical sound wave. If the oscillation of the oscillator is given by equation

(3.1)

where is elongation, is amplitude, is circular frequency and is time, then the sound waves generated, when observed at any point on the sphere with a radius , is defined by the equation

(3.2)

where is the radius of the sphere of the observed spherical wave and is the velocity of sound in the air. If the environment is homogeneous then the propagation of the wave will be equal in all directions, but for the purposes of observation it is enough to take just one direction. Then Eq. (3.2) becomes

(3.3)

   Propagation of the spherical sound wave is given by the following equation

(3.4)

that is

(3.5)

and the propagation of the plane wave along the -axis by the following equation

(3.6)

   The Eqs. (3.2), (3.3), (3.5) and (3.6) can be applied to light waves by the following meaning of the values. The elongation would present a disturbance of the electric or magnetic waves since they are mutually conjugated. Amplitude presents the amplitude of the electric or magnetic wave. In this case the circular frequency has the same meaning, while would be the speed of light instead of the speed of sound.
   We should pay especial attention to the Eqs. (3.4), (3.5) and (3.6), because they were used to derive the Lorentz transformation whose aim was to prove the contraction of the body moving through an ether and to explain the negative result of Michelson's experiment. Really, the above stated equations were treated as equations which describe electromagnetic wave motion, instead of sound wave motion. In considering the fact that these equations have the same form both for the light and sound wave propagation it is justifiable to state that the special theory of relativity can be derived on the basis of sound propagation instead of on the base of light propagation. In the special theory of relativity it is stated that there is no higher speed than the speed of light, not even the relative speed. It was the same with sound. A lot of time, effort and knowledge were required to break through the "sound barrier". For a long time it was considered impossible. Many had stated that an aircraft would simply fall apart on reaching such a speed. In spite of this many aircraft of different dimensions have broken that sound barrier carrying heavy loads. Now many state that there is no way of breaking through the "electromagnetic barrier", that is to obtain a speed higher than the speed of light in vacuum. It is debatable whether that statement is based upon the facts or incomplete and approximate mathematical equations. Has it not, in fact, been broken by the distant quasars, that, judging by their red shift, are moving away from us at three times the speed of light [16]?
   Sound velocity propagation does not depend on the speed of motion of the sound source. The same occurs in the case of the propagation of light. However, in certain circumstances the velocity of sound can be higher or lower than in the open air.
   Let us suppose that the sound source is located at the origin of an unmoving coordinate system (Fig.3.1) and let us say that a closed car moves in a straight line, along the -axis at speed . The sound pulse, generated at the origin of the system reaches the moving closed car after some time and passes trough the back wall into the air inside. From that moment the sound in the car moves from the back of the car to the front at speed in relation to the back wall of the car. In relation to the sound source in the coordinate system , from which it originated, this sound is now moving at speed , where is the speed of the car, and with it also the speed of air which carries the sound. In that way the sound velocity in relation to the source can be up to almost two times higher. If the car moves in the opposite direction to that of the sound, then the sound velocity in the car relative to the source would be . This occurs because the closed car carries medium - particles of air, whose oscillations transfer sound. If the car is open this phenomenon does not occur, and the sound is propagated at the same speed as in the surrounding open space independently of the speed and direction of motion of the open car. In a closed car or an airplane, whose speed may be higher than the speed of sound, the passengers can have a normal conversation and the speed of motion has no influence on the propagation of the sound inside the car or plane, because the particles, that transfer the sound by oscillation, are carried inside the closed space. If it where an open car traveling at supersonic speed then the particles would not be carried and the sound from the back part of that open car would not reach the front part. For example, it is well known that a sound of a jet stays behind the jet when the speed of the jet is higher than the speed of sound.

Fig. 3.1