Capacitors

Yes, but depends where. 

In tube amps and preamps is the only place where you are likely to actually run into this scenario.  In signal, as opposed to AC filtering, so long as you keep a 25% margin, get the smallest that’s appropriate.  

So if you have a signal that is nominally 300V then anything 400V or more is fine. 

However, in an AC power supply filtering applications having a cap which is higher than the peak of the AC waveform AND is intended to be a smoothing capacitor (i.e. used with pulsing DC)  is critical.   A cap which is not will short in minutes because the current, not the voltage, will cause overheating.

Just as background, film caps often can't get smaller than a certain V just because they are too hard to manufacture.  So your smallest V choice may still be greater than you need.  In speakers for instance, anything over 80V is fine, but I can't really find a film cap less than 400V

PS - DIYaudio is a great place for questions like this and has a bunch of friendly builders and modders who would love to help you out. 

Yes and no.

No in that even at 400 volts, you would well exceed the power handling capacity of all but maybe the most powerful amplifiers and 800 volts would just be more over-kill.

Yes in that the different voltage ratings are most certainly associated with different materials construction and many people can hear a difference in this aspect.

The answer to your question is an unequivocal NO. Unless you know amplifier as well as the designer, never substitute a lower voltage capacitor than the rating of the existing. Over voltage an electrolytic capacitor and it can explode. Over voltage a film cap and it can short. 

To calculate the capacitor voltage rating for crossovers, follow these steps:

1. Determine the maximum voltage that the crossover will encounter during operation.
2. Consider the peak voltage of the audio signal, which is typically higher than the RMS voltage.
3. Apply a safety margin, usually 1.5 to 2 times the maximum voltage, to ensure reliability.
4. Select capacitors rated for at least the calculated voltage to prevent breakdown.
5. Check the capacitor's temperature rating, as higher temperatures can reduce voltage tolerance.
6. Ensure the capacitor type (e.g., film, electrolytic) is suitable for audio applications for optimal performance.

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So, if an amp is rated at 1,000 watts into 8 ohms.

1,000 watts / 8 ohms = Voltage squared

=89.4 volts RMS

89.4 volts x sq rt 2 = 126 volts peak

126 volts peak x 2 (margin of error to be conservative) = 252 volt rating for the caps.

If you substitute 400 volt for 800 volt caps, they are still both way over-kill from most anything you will ever encounter.