The purpose of my experiment was to determine what parts of the soundboard on a piano resonate according to what kind of tone it is exposed to: high sounds, middle sounds, or low sounds. I took a microphone and placed it on the soundboard in three different positions. I then hooked the microphone up to a computer software that graphed resonance. I then began taking data. After finishing the experiment, I determined that the left side of the soundboard resonated the most when I struck any key, but the amount of each resonance varied between each key struck. The middle resonated the least.
The piano is one of the most basic musical instruments. Clavierís Piano Explorer (Clavier 1995) magazines talk about the earliest forms of the piano. It started out in the 1400ís as harpsichords that were made of strings that were plucked instead of struck. This advanced to clavichords with strings that were struck. Clavichords progressed into organs, which became the piano at the end of the 17th century. It was known as the pianoforte, later shortened to the piano. The piano started out very primitive, but was developed to include pedals, thicker strings, and a stronger frame to allow for greater sounds. Piano makers also experimented with shapes, finally settling on the grand piano or upright shapes typically seen today. All of these improvements allow for the range and strength of each sound. Although many people can play the piano, most normally do not know how the sound is actually created.
When it comes to the piano, or just sound in general, frequency and resonance are the reason for the sound. In the piano, the resonance of the strings is the source of the sound. But there are many other components in creating the tone. When a key is struck, the attached hammer hits the relative string, causing it to resonate. This in turn creates a pitch, or frequency, depending on the length and tension of the string. This pitch could be heard without anything else, but it would be very soft, and unable to be heard by a large crowd. When you look inside the piano to see what lies beneath the strings, you find a soundboard. The soundboard is a thin piece of wood, typically about 3/8" wide that rests inside the cabinet of the piano on the plate that merely strengthens the case. The soundboard is the same size as the case and supports bridges that in turn support the strings. When the strings resonate, the frequency is transmitted to the soundboard, which then resonates. Its resonance is what transmits the vibrations of the strings into the piano tones you hear. When looking at Dick and Raeís (Carpenter and Minnix, 1993) chladni plates experiments, I see the likeness of the soundboard to chladni plates. The chladni plates vibrate at different spots according to the frequency. The soundboard also vibrates at different spots according to what tone it is exposed to it. These different vibrations in the soundboard are what cause the sounds you hear to differ.
I am testing what parts of the soundboard resonate according to which key is struck and the frequency it transmits. I will do this by using a microphone placed strategically on different parts of the soundboard. The microphone will in turn be hooked up to a computer software programmed designed to graph sound and its frequency. Hopefully, if my project goes as planned, the graphs of each of the frequencies will vary enough to show me what part of the soundboard resonates most. As discussed in Hannís book (Hann 1991), every instrument produces different styles of graphs. Each is a wavy line with troughs and peaks. But as Hann points out, these peaks and troughs also show the change in air pressure, not just the toneís pure resonance. She also discusses the basics of sound waves and how, unlike ocean waves, they move horizontally. Any graph of any frequency will show this, just by seeing how the wave is sinusoidal. Each of my graphs will show a wave that is constantly moving horizontally, with changes in the vertical movement. MacCauley (Macaulay 1988) also talks a lot about interpreting graphs of frequencies, and what the different amplitudes and periods mean. I will then be able to determine what parts resonate according to the graphs given. If the period is smaller, I can see that the frequency is higher, thus determining that those parts resonate more for that tone. If the amplitude is higher, I will be able to tell that the tone is higher.
I believe that the parts of the soundboard closest to the resonating strings will resonate the most, for thatís where the vibration given off by the string will be the strongest, and thus the most influential on the soundboard. As seen in Giancoliís Physics book (Giancoli 1991), vibrations are periodic, meaning that they repeat themselves over the same path. But when friction, air pressure, and other such natural forces are taken into account, the amplitude and period become smaller with each oscillation, or vibration. Thus, it can be concluded that the farther away the original frequency from the different parts of the soundboard, the weaker the frequency will be. My experiment will test to see just how accurate this assumption is, and even to test if there are different frequencies and graphs from different notes. It will also be testing if different parts of the soundboard even vibrate, or if the same parts of the soundboard vibrate each time any note is struck.
I think that when the microphone is placed on the soundboard, the lowest C will have the highest resonance compared to middle C and high C. Also, high C will have a higher resonance than middle C. I also think that the position of the microphone will affect the resonance of each note. When the microphone is placed directly in the middle of the soundboard, it will have the least amount of resonance because the outsides will have more ability to move than the middle because it has less around it to affect its movement. The left side of the soundboard will resonate the most because it is closest to the lowest pitches and has the widest width. The right side will resonate more than the middle, but less than the right side, because it has a smaller width, higher frequencies, and also has a board that sits a little above the soundboard that helps to dampen the highest sounds to avoid ear-splitting sounds. The four holes that release the sound each have different diameters, which also will affect how much sound is released from each hole. The hole with the largest diameter, which is the hole in which I will be placing the microphone, allows for the greatest amount of sound to be released (of the four).
††††††† †† Set-Up
My set-up is roughly as follows. I will bring my computer into the room where my piano sits. I will open the SoundView program I have from the Internet. I will hook a PlainTalk microphone up to the IMAC computer. I will then set the microphone on various parts of the soundboard of the piano and then begin collecting data. (See diagram).
The conditions of the room when I will take data is as follows: the piano to be tested is a baby grand Yamaha piano with the lid completely open as far as it can be open. The microphone will be placed directly on the soundboard. I will be careful to mark the exact location of the microphone and not move it until I am completely done with it in that spot. I will test each key in that position before moving it to the next position. I will test three positions. The first is the far left of the soundboard, right in the middle of the last string. The second is in the middle of the soundboard, roughly in the middle of the strings. The last is the farthest right, towards the back of the soundboard, in one of the four holes. I will also be careful to start recording only when complete silence could be obtained to avoid any outside sounds altering my graphs.
I will start by marking three places on the soundboard, each approximately in the middle of the board to allow consistent data to be taken. I will then choose three notes, each the same pitch: C. The first C is the lowest C on the keyboard, the second is middle C, and the third is the highest C on the keyboard. This helps allow for data that is relatively consistent with similar frequencies. After connecting the computer to the microphone and the SoundView program, I can start taking data. First, I will strike the lowest C with the microphone in the farthest left position. Then I will continue until each position has been tested with each note.
Not only will I test the resonance of the pitches with the lid fully open, I will try to close the lid partially and see how this affects the frequency. (I am not going to focus on that, though, because the only effect it has on the waves is that the sounds fades away quicker.) Then I will try to push the damper pedal and hold it down while I recorded the sounds. The una corda pedal is also known as the soft pedal. When the hammer strikes the strings, it typically strikes three strings. But when the damper pedal is pushed, it moves the hammer over so that when a note is pressed, the hammer only hits two strings. This creates a softer sound. (However, I will not focus on this either, because when I test this variable, again there isnít that much of a difference. The waves are all smaller, because the sounds are softer and again it fades out quicker because there are fewer strings to vibrate.
††††††† †† Results
To determine which part of the soundboard resonated the most, I had to first compare each graph and see which part resonated the most. To determine when the sound first started (to ensure that the graphs were taken simultaneously), I took my metronome and turned the dial to sound out the sound of A (440 hz) and played that for two seconds and then hit the note. The pure tone of A always gave the same sinusoidal wave before changing according to whichever key was struck.
When comparing the graphs of the different microphone positions, I was able to determine the motion of the soundboard by the amplitudes of the waves. When the bass (or low) key is first struck, the amplitude is the largest in the graph of the left microphone position (LMP), meaning that the left end of the soundboard resonated the most. Immediately following, the amplitude of the middle microphone position (MMP) was the greatest of the three. The middle of the soundboard resonates the greatest, but only for a split second. The amplitude of this graph also doesnít ever get as high as the amplitude in either of the other two graphs. Next, the amplitude of the graph of the right microphone position (RMP) was the largest of the three. Thus, the right side of the soundboard next resonated the most. This pattern continued: resonance in first the left, then middle, then right side of the soundboard. It can also be determined that when the bass notes are struck, the ends of the soundboard resonated the most.
When the middle notes were struck, I was able to determine by looking at the amplitudes of the graphs that the ends of the soundboard resonated the most. In this case, when the middle note was struck, the amplitude was the largest in the graphs when the microphone was in the LMP or the RMP. The middle of the soundboard acts as a fulcrum to the outer edges. This was determined by the fact that the amplitude of the graph of the MMP showed little oscillations. The movement of the soundboard is basically a see-saw between the two ends, however, the left side of the soundboard did resonate more than the right side did.
When the highest notes were struck, I was able to look at the graphs of the microphone to determine that the left side of the soundboard started off with the strongest vibrations. The amplitude of the graphs started off large, but quickly faded away to almost a straight line (as straight as it could get considering the margin of error). The right side of the soundboard started with a medium amplitude, but jumped for an instance to a higher amplitude before it also quickly dropped off to a straight line. The middle of the soundboard had a medium amplitude before it too dropped until it was a straight line. No part of the soundboard seemed to dominate in vibrations when it came to higher pitched tones. The whole soundboard seemed to vibrate quickly and then fade away rapidly. It can be compared to a trampoline in that it seemed to be taking the other sidesí vibrations. It canceled itself out until it was hardly moving at all.
It is quite possible that there were errors in my procedure. For one, the microphone I was using was new and quite sensitive to outside noises. Although I waited until complete silence, any movement whatsoever would mess up the soundwaves being emitted. Even my breathing affected the soundwaves that were picked up by the microphone. Also, all objects in the room where my piano sits would absorb a small amount of the sound. Just like the una corda pedal, it affected the final graphs. Plus the height of the lid of the piano affects the sound. The higher the lid was raised, the more sound it released. Not to mention how hard I struck the keys each time. I tried to strike the keys with equal pressure each time. And since I am a skilled piano player, I have the ability to get a certain dynamic level with most notes, but since it was not a perfectly equal amount of pressure, data could be slightly off. Also because the microphone position was not guaranteed to be at the exact middle of the soundboard, with the exact distance from the outsides, I cannot accurately determine the "left", "right", or "middle" of the soundboard. I also did not take into account the fact that the soundboard could resonate from the front to the back, not just left to right. I must also take into consideration that even though I chose three keys that have the same pitch, my piano may be slightly off tune and even the slightest difference in tones could affect my data. One thing that would have been a better way to take data would to have taken three microphones with computers to take data at the same time with the same sound. But this would have required money and resources that I do not have.
When a graph has waves that are close together, there is a higher frequency. Higher frequency means that the sound is stronger. When a graph is taller, it has higher amplitude. As Hann says, "different sounds are carried on the wave by tiny changes in the amplitude" (Hann, 1991). Giancoli describes these kinds of waves as transverse waves (when they are sinusoidal waves).
After having looked at the data and seen what parts of the soundboard resonate according to which sounds are played, I began to think. Why does the resonance of the soundboard really matter? How does it confirm what the ear hears when a note is played? How does it affect the sounds of the piano? Well, to answer these questions, I must look and see how soundwaves affect the ear. We are told by scientists that when a key is struck, the force of the strike causes the soundboard to vibrate, which is what causes the sounds that we hear. So I guess the real question is how does the resonance of the soundboard cause the different pitches that we hear? Anyone who looks into the back of the piano can see the different strings. The lower notes have only two strings that are much thicker than the highest strings, which have three very thin strings. The bass notes have very tiny wires that loop around the strings to add even more thickness, whereas the soprano notes are only a thin wire. The length of the strings then breaks it down further. Instead of having many notes with the same width of strings, the length differs. The longer and thicker the string, the deeper the sound emitted. When the strings are struck, these different strings then emit the different vibrations, because the strings have different widths. This causes the soundboard to vibrate in different places. These different movements of the soundboard are what cause the different sounds.
Being a pianist, I understand a lot about the differences between high sounds and low sounds. But as anyone can determine what is a low sound and what is a high sound, people donít often understand more than that. When playing a low sound, it is much easier to play it loud and then it holds out a lot longer in comparison to high sounds, which are hard to play loudly. This is much like singers. Singers often have more difficulty singing high sounds in comparison to low sounds. These differences in sound can be determined when looking at the graphs of the resonance of the soundboard. Lower sounds incorporate the entire soundboard and at one point or another, each of the three sections of the soundboard vibrates more than the others. There is no one dominating section. Not only does this allow for more sound, but it also allows the sound to hold out longer, because it takes longer for the whole soundboard to stop vibrating compared to a small section. There are other parts of the piano that contribute to these attributes of lower sounds, but the soundboard does contribute a large part considering it is what "transmits string vibrations into piano tones" (Claviers, 1995).
Next, I will look at the higher notes. When a high note is struck, because of the shape of the soundboard and how small it is on the right side and the length and thickness of the strings, the whole soundboard begins to vibrate. (I am not exactly sure of why this happens, but that was not what I was testing). Because the whole board begins to vibrate, it competes with itself to vibrate. Just like when two people are jumping on a trampoline, not everyone can bounce high at the same time, or they take each othersí bounces and level out the trampoline. That is exactly what happens here. The soundboard competes with itself and then cancels itself out. That is why high sounds fade out much quicker and are harder to hear. Also to be taken into consideration is that the thicker the string, the more energy it can store. So because these strings are way thinner, they can store less energy and not continue to resonate and be heard as long as the bass notes. The bass notes can store more of the energy from when the hammer struck the strings because there is much more wire to store the energy given from the hammer. (That also begins to go into how high of pitch the human ear can hear and how it is harder to hear these higher sounds).
When looking at the middle notes, it happens much like a seesaw. Both ends vibrate the most, with little vibrations in the middle. The middle acts as a fulcrum to the outer ends. The sounds we hear are balanced and right in the middle range, because the soundboard has the most even pattern of vibrations on each end. The only reason that one end vibrates more than the other is because of the shape of the soundboard.
Now, anyone might ask, why would I even care what part of the soundboard resonates? Well, for me, as a pianist, it is interesting to learn where the sounds I play come from. But for those who do not play the piano, this idea can be incorporated into sounds we hear all around us, like the radio. Through my experiment, we can see that lower notes (bass notes) cause more resonance and higher amplitudes in soundwaves as compared to higher notes (soprano notes). This explains why when you hear someone driving by with their music turned up really high why you can feel the bass but not hear the soprano notes. The bass notes cause a higher amplitude in the soundwaves and can thus cause more of an effect on the listener.
Bird, Steve. "SoundView". <http://www.physics.swri.edu/SoundView/>. Sept 14, 1997.
Carpenter, D. Rae, Jr. and Minnix, Richard B. Dick and Rae Physics Demo Notebook. Dick and Rae, Inc.:
Lexington, Virginia. 1993.
Clavier. Piano Explorer. September 1995.
Giancoli, Douglas C. Physics Third Edition. Prentice Hall: New Jersey. 1991.
Hann, Judith. How Science Works. The Readerís Digest Association, Inc.: Pleasantville, New York. 1991.
Macaulay, David. The Way Things Work. Houghton Mifflin Company: Boston. 1988.
Last revised: 5 June 2001