Hi Bruce,
What will double, as seen by the amplifier, is the impedance that each speaker has at any given frequency. "Impedance" reflects the combined effects of resistance, inductance, and capacitance at that given frequency. Assuming that the two speakers have the same impedance (as each other) at all frequencies, half of the voltage that is put out by the amplifier at any given frequency at any given time will appear across each speaker. Think of the output of the amplifier as the summation of many different frequencies occurring simultaneously. Half of the voltage corresponding to each of those frequencies will appear across each speaker. The summation of all of those halved voltages, appearing across each speaker, will be the same as what the amplifier is putting out, except scaled down by a factor of 2.
Something that may help to clarify this would be to consider what happens if a voltage at some frequency is applied across two series connected resistors, or alternatively across two series connected inductors, or alternatively across two series connected capacitors. In each case, half the voltage appears across each of the two series connected components. And likewise if the components are a complex impedance consisting of some combination of resistance, inductance, and capacitance, such as a speaker. And in each of those cases the phase angle between voltage and current at any given frequency will be the same as if only one of the two components were present, since the two components have identical phase characteristics.
Concerning parallel connection, if the amplifier is solid state and therefore has a negligibly small output impedance, the speakers essentially become independent of each other, and have no effect on each other even if they have different impedance characteristics. The load on the amplifier will be increased, of course. In the case of a tube amplifier that has significant output impedance, paralleling non-identical speakers having significantly different impedance vs. frequency characteristics could result in some alteration of the frequency response of each speaker, because the voltages appearing at the output of the amp would be affected by the relation between the amp's output impedance and the total load impedance.
Viral, no, you would need an amplifier rated at 100 watts into 8 ohms to put 50 watts into each of two series connected 4 ohm speakers. If the 100 watt amplifier is solid state and therefore has negligibly small output impedance, and is robustly designed and is capable of supplying lots of current, it would be able to put 200 watts into a single 4 ohm speaker. The 1/4 factor is the relation between the power into each of two series connected 4 ohm speakers (50W in this case), and one 4 ohm speaker (200W in this case, provided by an amplifier that is rated at 100W into 8 ohms, but is presumably and hopefully capable of providing 200W into 4 ohms).
Whether or not you would want to put 50 watts into the speakers is a separate question, of course, which depends on their efficiency, the listening distance, the kinds of music, your volume preferences, etc.
Best regards,
-- Al
