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The Doppler theory states that sound waves change in frequency depending on the relative speed and movement of the observer. If the sound moves away from you the waves expand and produce a different pitch or frequency, the reverse is also true. Through a device, essentially a tube with a whistle on one end, Mach was able to demonstrate Doppler's theory. Mach would then theorize that this would apply to light as well lead to the possibility of studying star's based on their light spectrum.
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Mach bands are light illusions created when similar gradients are placed next to each other. Say you have a dark grey block and a lighter grey box, placing them next to each other will produce a lighter area where they meet and a darker area at the edges. Mach proposed this happened do to "retinal points perceiving themselves as above or below the average of their neighbors." Perception itself is just observing the relations between stimuli. This would go on to influence Mach's philosophy.
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Mach's principle, stated simply, is that an objects inertia is related to all mass within the universe. Motion and space relied on each other and were not absolutes. Inertia was not a quality inherent in an object, inertia was the object reacting to it's relationships. While Mach's idea went against the established Newtonian understanding of absolute and fundamental space, it was this distinction about space and it's required relations that would lead to Einstein's theory of general relativity.
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Mach is probably most famous for his capturing and articulating of motion relative to sound. If an object moves at the speed of sound it moves at Mach 1. He also worked out that supersonic speed depends on the fluid or substance an object would move through. Again, this would demonstrate to mach the necessity of looking at the world in terms of relations and relativity. Through his study of supersonic speed Mach also developed new high-speed capturing techniques.
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Gregerson, E. (n.d.). Ernst Mach. Retrieved December 27, 2020, from https://www.britannica.com/biography/Ernst-Mach
Pojman, P. (2019, March 03). Ernst Mach. Retrieved December 27, 2020, from https://plato.stanford.edu/entries/ernst-mach/
Rothman, T. (2018, February 27). The Forgotten Mystery of Inertia. Retrieved December 27, 2020, from https://www.americanscientist.org/article/the-forgotten-mystery-of-inertia -
Sixtysymbols. (2017, May 11). Mach's Principle - Sixty Symbols. Retrieved December 27, 2020, from https://www.youtube.com/watch?v=cPEwkMHRjZU
Sound: Crash Course Physics #18. (2016, August 04). Retrieved December 27, 2020, from https://youtu.be/qV4lR9EWGlY?t=450
