Hi Abhishek Anand ,

though the speed of the wave is independent of the speed of the source in both cases, the details are different for sound and EM waves:

Assuming that the sound propagates in a gas (or fluid), and that the flow of the gas is homogeneous (no divergence, no curl), then there is one "rest frame" defined by the fact that the gas is resting as seen from this reference frame. Sound waves are not inertial objects (in contrast to the the ball you mentioned) but disturbances of the density of the gas. Measured from the rest frame, the speed of the sound waves depends mainly on mass, density, and thermal velocity (i. e. temperature) of the gas molecules. Pictorially speaking, the source reaches out just to a thin layer of neighboring molecules, the further propagation is independent of the source and the initial speed of the molecules. Seen from other inertial frames, the velocity of the sound propagation and the velocity of the frame relative to the rest frame add up vectorially. So, if the source is moving relative to the rest frame in, say, positive x-direction, then an observer moving with the source will see the sound propagating slower in positive x-direction, and faster in negative x-direction.

EM waves (in vacuum) are not disturbances propagating in a surrounding medium but carry their own medium (electromagnetic energy) with them. The speed depends on the permittivity and on the permeability of vacuum, and since these quantities are the same in all inertial frames, the speed of EM waves is the same in all frames. Consequently, there is no special "rest frame".

To put it another way, that the speed of light is the same in all inertial frames is a postulate of Special Relativity Theory (SRT), and since SRT wasn't refuted experimentally until now, this postulate seems to be correct.

That observers moving at different velocities relative to a source do not make contradictory measurements is based on the fact that there is no simultaneity among different frames; instead, an observer looking at a moving source will see the region behind the source at an advanced time, and the region in front of the source at a delayed time.

Since this is counter-intuitive, a thought experiment might serve as illustration: Imagine a long railroad carriage, with two light detectors and a firecracker in the middle, and two light sources at the front and the rear, at equal distances from the middle. The light detectors and the firecracker are connected by an electronic circuit which ignites the firecracker if both flashes arrive at (nearly) the same time. Suppose that seen from the carriage, each light source emits a flash simultaneously; due to the equal distances, the flashes of light arrive in the middle at the same time. So, the cracker explodes.

If the carriage is moving very fast (e. g. c / 2 :-) an observer resting relative to the rails would see that the flash from the rear has a longer distance to travel than the flash from the front because the middle moves a bit forward during the propagation of the flashes. If general simultaneity existed, the outside observer would see that the flash from the rear arrives later, and the firecracker is not ignited.

But the firecracker cannot be in two different states for the two observers! (The carriage could stop later on, then both observers were in the same frame. At least now, the firecracker has to be either exploded or not.) The solution is that the outside observer sees the flash from the rear starting first, and the flash from the front starting later, and he agrees with the observer on the carriage that the flashes arrive at the middle simultaneously, and the firecracker explodes.

Hi Abhishek,

In case of Wave propagation, the speed is due to the two fact Group Velocity and Phase velocity. We can have a different phase velocity with respect to different observers but the Amplitude is ultimately governed by the Group Velocity, and It appears same irrespective of speed of the source.

Joerg Fricke 's explanation is good, but I thought I would add that it has been found that everyone measures the speed of all electromagnetic energy in free space to be the same relative to them, no matter what speed they are travelling or which direction. This is very strange and hard to explain - it doesn't seem to make sense. Special relativity is an explanation of this that has been found to work in all cases, so is the generally accepted theory. It says that things travelling at different speeds experience time differently. This is a very strange idea, but gives results that agree with the strange measurements.