The experiment that provided evidence for the stretching of light waves, known as redshift, was the observation of the spectral lines of distant celestial objects. This experiment is based on the phenomenon called the Doppler effect.
The Doppler effect states that the observed frequency or wavelength of a wave changes if there is relative motion between the source of the wave and the observer. When an object emitting light is moving away from an observer, the wavelengths of the emitted light appear to be stretched or shifted towards the red end of the spectrum. This is known as redshift. Conversely, if the object is moving towards the observer, the wavelengths appear compressed or shifted towards the blue end of the spectrum, known as blueshift.
In the early 20th century, astronomers began observing the spectra of distant galaxies. They noticed that the spectral lines, which represent specific wavelengths of light emitted by elements in those galaxies, were shifted towards the red end of the spectrum. This observation suggested that these galaxies were moving away from us. Furthermore, the more distant the galaxy, the greater the observed redshift. This led to the realization that the universe is expanding, and the redshift of light from distant galaxies provided evidence for the Big Bang theory.
The redshift of light is not related to the stretching of sound waves, as sound waves require a medium to propagate, while light can travel through a vacuum. Instead, the redshift of light is a consequence of the expansion of space itself.