Because different instruments have different timbres, each type requires specialized amplifiers. This has given birth to the many amplifier types that are available on the market today, including guitar amps (which also branch out to acoustic and electric guitars), bass amplifiers, acoustic instrument amplifiers, keyboard amplifiers, drum amplifiers and multi-purpose amplifiers. While multi-purpose amps can usually get the job done regardless of the instrument, specialized ones provide better sound, case in point are tube amps for electric guitars.
These are amplifiers especially made for guitars, with the purpose of coloring if not changing the resulting tone. They are available in combo or stack format. Combo amps are the most common because of their portability and convenience, these ones house both the amplifier section and speaker section in one cabinet. The "Stack" format feature dedicated housings for the amplifier section, called the amp head, and speaker cabinets. Further distinctions of guitar amps include solid state vs tube circuitry, and there's also the latest digital modeling amplifiers that mimic the behavior of multiple amps packed in a single form factor.
As the name implies, these amplifiers are especially built to handle the low frequency thump of electric bass guitars. Much like guitar amps, they come in two configuration, either combo or stack, and usually feature the same essential controls as guitar amps. Since getting the bass sound right requires bigger and more powerful speakers, these amplifiers are generally on the heavier side.
Acoustic amplifiers are specifically designed to handle the dynamics and nuances of acoustic instruments, be it acoustic guitar, acoustic piano, fiddle and many more. These amps lean towards a more neutral sound that can be used for other applications as well, i.e. for vocals. The result being a good amp for singer songwriters who play and sing in small venue settings.
Since keyboards and synthesizers have extended note and frequency ranges, manufacturers have built specialized amplifiers that can handle varying sounds and notes that they produce. Unlike guitar amps that shape the sound, these amplifiers are very transparent to ensure that you hear the actual sounds of the keyboard or synth without any coloring. In some setups, keyboards are just plugged straight into the PA, but having a dedicated amp allows for more clarity and separation from the vocals, as well as better on-stage monitoring for the keyboardist.
These are called both Drum Amplifiers and Electronic Drum Amplifiers. They have two main uses; amplifying electronic drums and being used as powered stage monitors by drummers. They are similar to Keyboard Amps in that they can faithfully reproduce a wide frequency spectrum with the added benefit of being able to handle low frequency transients much better - EG kick drums. Some also come with other drummer friendly features such as using a wedge shaped form factor or having control knobs which can be adjusted using drum sticks.
Multi-purpose amplifiers are mostly like keyboard amps, providing straightforward transparent amplification for any type of instrument - including Saxophones, flutes, ukuleles and more. These are ideal for multi-instrumentalists and venues that host events that feature various instruments. Modern powered speakers with their dedicated preamp and controls, fall under this category. And in today's digital modeling driven world, many guitarists and other musicians have been opting for these types of amps, while getting their tone coloration from amp modeling units like the Kemper Profiler and Axe FX.
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