In a gravitational wave detector using laser beams and interference patterns, length of interferometer's arms change when gravitational waves pass through the detector. This is supposed to happen as ds2=gμν dxμ dxν and gμν changes by the influence of a gravitational wave. This is in contrast with an usual optical interferometer device, where length of the arms of the interferometer remains fixed, and using interference patterns, one obtains useful information on the wavelength of light source.

I respect your argument ......That is how we detect gravitational waves in practically. In your answer , it didn't explained why  gravity moves same speed as light ...!.. ,   There is no way to  prove gravitational  wave is same as  behave as electromagnetic waves. What i want to know is  why  gravitational waves  take same as  speed of light !..  then  gravitational propagation  can be  consider as  EM  propagation.  If  the  gravity propagate  EM  wave  ....so  we can use radio detector  to  detect  gravitational wave  !

Dear Manoj : you can find an interesting answer by considering gravitomagnetism, which transposes electromagnetism into gravity, by remarking that Coulombs law is similar to Newton's law.

However, Newton didn't make a difference between moving masses and stationary masses in his gravity theory.

In gravitomagnetism, many events can be succesfully explained, by considering the speed of masses as causing magnetic-like fields. These fields have the dimension of Hz.

The most easy representation is a spinning sphere (Sun), which influences the orbits of planets, by pushing them to the Sun's equatorial plane.

However, the proof of propagation at the speed of light is still not made.

More information annexed.

https://www.amazon.com/Causality-Electromagnetic-Induction-Gravitation-Gravitational/dp/0917406230

http://gsjournal.net/books/De-Mees-Gravitomagnetism-and-Coriolis-Gravity-2011-A4.pdf

@Manoj,

beside electromagnetic and gravitational interaction there are weak and strong interactions. All, according to the best existing theories, propagate in vacuum with speed c.  This, of course, hints to some communality of all these interactions. Perhaps there is some infrastructure in the background such as a 'spin network' on which all these types of interactions exist as various types of processes. Such hypothetical considerations should not mislead us to ignore the differences between distinct entities. In the case of electromagnetism and gravity the simple truth is that gravity comes from mass and electromagnetism from charges and currents. (This is the 'simple truth'; the 'truer truth' says that gravity comes from all energy, and therefore, with much lower strength though, also from charges and currents).  

Only electromagnetic waves can have  speed of light  isn't?

Dear Manoj, it is accepted that not only electromagnetic waves can have the speed of light, but also the electric field (separately) and the magnetic field (separetely).

However, to get the proof of that, one must make a test between two reference frames, of which one is moving.

If an electromagnetic oscillation from one refrence frame is measured by the second one (which is moving at constant speed), one comes to the Lorentz Transformations, which contain the speed of propagation.

If a real test is made and one comes to the a speed of propagation that matches the speed of light, then it is proven that also the electric field (separately) and the magnetic field (separetely) propagate at the speed of light.

The same could be done for gravity fields and gravity waves, but it is much too early to get answers that confirm that all these propagation speeds match the speed of light.

However, it is considered as "probable".

I think the  Albert Ernestine   knew  empty  vacuum  as  a  common   relative reference to  all others .  Without vacuum there is no any  meaning to the relative reference ! . Then vacuum became      absolute   sense !.   Therefor it is natural  that  speed  of light  is   constant  in a vacuum . Soon  speed  of light  is constant  for  all  inertial reference system.

(1) But gravity  makes more trouble  !  .. as it travels speed of light  . Because only  electromagnetic wave can have  speed of  light  .  Therefor  it is natural to think  that   gravity is connected  to  an  elector magnetic fields..So  it is glimpse to a kind of a unifying   picture  to  gravity in  with elector magnetism .!

In Tousson’s Electrodiscrete Theory, gravity is just an imbalance in the electromagnetic force caused by the discreteness of space and time. This result has come out of the theory. It has not been the starting point. See the link below.

Book:

https://drive.google.com/file/d/0B6DMVPT39yx7ZTc0blRMQ194Qlk/view?usp=drivesdk