will a pulse retain its shape as it travels through the medium ???
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the pulse will not retain its shape as it travels through the medium because a pulse is made up of harmonic waves having large range of wavelengths which travel with different speeds in the medium .
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A pulse is made of harmonic waves with a range of wavelength. As the speed of propagation in a medium depends on a wavelength, different wavelength components of the pulse travel with different speeds. Thus the pulse will not retain its shape when it travels through the medium.
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