Physics Puzzle: Inside a Piano
April 23rd, 2009
| Categories: Music and Audio, Physics Puzzles
We all know that when you press a piano key, it triggers a hammer inside the piano which strikes a string, producing its distinctive sound. However, a closer look inside a piano will reveal that the hammer strikes more than one string simultaneously. Here is a portion of an image taken from wikimedia showing the inside of an old upright:
Looking closely, you should be able to observe not one, but three strings per hammer. Can you try and guess why that is so?
EDITED, 25-Apr-2009: An explanation has been added in the comments - view them to see it.
Would one string not offer enough resistance? i.e. it would just bend with the hammer rather than vibrate? More strings increases the elasticity (right term?) without changing the pitch. I notice the middle strings have two per hammer, and the lowest have only one. The greater mass per unit length (and possibly differences in tension) would eliminate the need for extra strings.
I know the strings are tuned just slightly differently. I don’t really understand all the reasoning behind it, but I do know that one advantage is that this allows for longer sustain of notes. If a string stops oscillating before its sister strings (because piano hammers are imperfect, and so each vibrating string will have a different amplitude), it will still be coupled to the bridge and subsequently the other strings for that hammer, which will “drive” it to oscillate once more. The exact tuning of the notes to encourage this oscillation is determined by how the strings interact with the bridge, but I won’t pretend to be able to understand the determining factors.
Interestingly, and I don’t know if this is related at all, but piano’s are tuned slightly incorrectly on purpose. If each note were tuned to its exact frequency, the piano would sound funny to us. By use of mathematically calculated imperfection, the piano can play in all keys.
jbrydle,
Good job observing the number of strings. The reason there is only a single bass string is that more can’t be fit in there! A bass string is about a third of an inch in thickness - there just isn’t enough room to squeeze in three. Even if you could, once you got them to vibrate they’d just bump into each other.
Your hypothesis about the strength is also incorrect, as can be deduced by looking inside a grand piano. Grand pianos have a “soft” pedal, which basically moves the hammers a bit to the side, making them strike just two strings (or even one) - this quietens the piano sound. So it seems the pedals CAN strike a single string without any worries of damaging it.
MCSafety has got the right idea without articulating the physical mechanism - can you try and guess it? If not I’ll post a solution in a day or two.
PS
The slight mis-tuning of the piano keys relative to each other has nothing to do with the fact there are three per hammer - that’s a whole different story!
The piano produces a sound by a hammer striking a string (or a bunch of them). The strings are connected to a piece of wood called the Soundboard, and make it vibrate as well, which is what produces the piano’s sound (the strings themselves do NOT produce it).
When building a piano, it’s a loudness vs. sustain (i.e., how long a note sounds while holding down a key) war - both are desirable, but contradictory. The more energy a string gives away to the soundboard, the louder the sound will be, but the faster it will decay.
To solve the sustain problem, piano builders have been putting in three strings, slightly detuned (by about a Hertz, give or take) relative to each other. Once struck by the hammer, all three strings begin vibrating. Initially, they all sound it; however, due to the phenomenon of beats, the oscillations quickly become out-of-phase, after a time approx. ~ 1/Hertz ~ sec. This means the forces the strings apply on the soundboard tend to cancel out each other, conserving energy within the strings and not giving it all away at once, hence enhancing sustain.
This can also be understood in terms of acoustic impedance. Adding three strings makes sure there is some impedance mismatch between the strings and the soundboard, which causes some sound energy to be reflected back to the string system, conserving it and making sure it seeps away at a more moderate rate.
Dear Assaf,
I’d like to know what frequencies are these 88 strings (or group strings).Are they single frequencies? Or fundamental frequency with harmony?
what are the numbers?
Thank you
Jian Zhang
Are you asking how the strings on the piano are tuned, or how the three strings in a particular key are tuned? If it’s the first, there’s a table in Wikipedia:
http://en.wikipedia.org/wiki/Piano_key_frequencies
As for the second, I’m unsure - I’ve never tuned a piano myself, so the exact detunings are beyond me. You’ll have to ask a piano tuner.