Carbon microphone
The first microphone that enabled proper voice telephony was the (loose-contact) carbon microphone (then called transmitter). This was independently developed around 1878 by David Edward Hughes in England and Emile Berliner and Thomas Edison in the US. Although Edison was awarded the first patent in mid-1877, Hughes had demonstrated his working device in front of many witnesses some years earlier, and most historians credit him with its invention.
Horn loudspeaker
The physics (and mathematics) of horn operation were developed for many years, reaching considerable sophistication before WWII. The most well known early horn loudspeakers were those on mechanical phonographs, where the record moved a heavy metal needle that excited vibrations in a small metal diaphragm that acted as the driver for a horn. A famous example was the horn through which Nipper the RCA dog heard "His Master's Voice". The horn improves the loading and thus gets a better "coupling" of energy from the diaphragm into the air, and the pressure variations therefore get smaller as the volume expands and the sound travels up the horn. This kind of mechanical impedance matching was absolutely necessary in the days of pre-electrical sound reproduction in order to achieve a usable sound level.
The megaphone, a simple cone made of paper or other flexible material, is the oldest and simplest acoustic horn, used prior to loudspeakers as a passive acoustic amplifier for mechanical phonographs and for the human voice; it is still used by cheerleaders and lifeguards. Because the conic section shape describes a portion of a perfect sphere of radiated sound, cones have no phase or amplitude distortion of the wavefront. The small megaphones used in phonographs and as loudhailers were not long enough to reproduce the low frequencies in music; they had a high cutoff frequency which attenuated the bottom two octaves of the sound spectrum, giving the megaphone a characteristic tinny sound.