Reflection of Waves: Is the Pulse Inverted?

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A pulse reaches the boundary of a medium in which the speed of the pulse becomes higher. Is the reflection of the pulse the same as for the incident pulse or is it inverted?
Also, does pulse refer only to mechanical waves and not to electromagnetic waves?
 
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I'm guessing you compare the difference in the index of refraction along the boundary. In general, if the index of refraction is smaller, the speed of the wave will be higher. If a wave reflects off a body of a lower index of refraction, no phase change occurs (the wave is not inverted). I wrote this while thinking of EM waves, but the general idea should be similar in the case of mechanical waves (a pulse could occur in any kind of wave).