What makes some instruments louder than others?

Question

Main question: are longer pianos actually louder?

Context: When a musician plays on an acoustic instrument, I expect that the loudness produced corresponds to raw energy (as measured in Joules or Watts if taken per second) that the musician puts in. Thus, timpani are usually louder than a recorder (flute), because a mallet hit can have a lot of energy, while if you blow into a recorder too much, it sounds different.

But then, when playing loudest possible sounds, is a trumpet player putting in more energy/power (in terms of air flow) than harp player (plucking strings)?

I would guess a lot depends on the definition of loudness and psycho-acoustics, because timpani sound to me louder than a snare rimshot despite having less decibels. Dispersion of high frequencies is probably why flutes sound so loud up close, but not so strong from afar. On the other hand, the instrument in question certainly matters, e.g. soft vibraphone mallets will absorb more energy than hard wooden mallets.

Yet, even if we get two similar instruments – two acoustic grand pianos from the same manufacture but of different length – my personal impression is that the longer one is audibly louder. Maybe the bigger one has harder hammers, I don't know, but I doubt it. Usually, even among different brands, bigger pianos seem to me "on average" (in my small anecdotal sample) louder than smaller ones, despite me putting in similar amounts of energy/power. Is this only subjective, or perhaps there is a physical reason behind this?

So, are longer pianos actually louder (in terms of decibels, watts, loudness units, etc.)? Why is it so, or what makes them seem louder?

Answer 1

Musical instruments are transducers, which means they change one kind of energy into another. All transducers have an efficiency, which means during the change of energy, some portion of the input energy is lost.

So putting 5 watts of mechanical energy into a musical instrument doesn't mean you're getting 5 watts of acoustic energy out. You'll get less than 5 watts. So right away, we know different instruments have different efficiencies and therefore produce different amounts of acoustic power. In the case of the longer piano, that means a larger soundboard, which increases the efficiency of the power transfer.

There are also different mechanical input systems for musical instruments that allow humans to put in different amounts of mechanical power in the first place. Also energy may be stored and released later (e.g., bagpipes, human-powered pipe organ) to allow for greater eventual output.

Finally, as you note, different frequency spectra have different psychoacoustic effects and loudness is a subjective perception of hearing that is affected by psychoacoustics.

Answer 2

They can be, but that is not the point of having them.

Musically, the point of having a larger soundboard, easier key action, etc. is not to be able to play louder. Any competent pianist can already play as loudly as appropriate for most compositions on any grand piano.

Rather, the point is achieving the same volume with less effort. The more effort you have to expand to achieve an outcome, the less control you have over the nuances of your performance. And nuance is exactly what distinguishes acceptable from great musicians.

So the point of having instruments that can be very loud is not to exploit that extra loudness, but to be able to control your performance better at the same loudness.