Section: Monday / Tuesday (circle one) Name: Partners: PHYSICS 07 LAB #: PERCUSSION PT Equipment: unction generator, banana wires, PASCO oscillator, vibration bars, tuning ork, tuned & un-tuned marimba bars, LoggerPro, LabPro, & Vernier microphone, make-shit mallet, ruler OBJECTIVES. Relate a bar s modes to its length and identiy whether or not they re harmonically related.. Compare tuned and un-tuned bars. Overview The possible vibrational modes o a string are easy to picture: one hump, two humps, three humps and they re all evenly spaced. Similarly, their requencies o oscillation are evenly spaced, i.e., members o a harmonic series. The vibrational modes o a thin bar are qualitatively similar, but the bar s stiness makes shorter and shorter wavelengths increasingly diicult to support and makes the associated requencies considerably higher. While a struck or plucked bar may have one or two particularly strong modes, and thus produce identiiable pitches, they are not harmonically related, so they are not perceived to be aspects o a single, complex musical sound. When musical instruments do make use o struck bars, those bars are oten modiied to enhance and approximate harmonically-related modes. Readings: Reading: Section 9.4 Bar clamped at one end Background A bar o rectangular cross-section that s anchored at one end and ree to move at the other is expected to have its lowest requency o oscillation be 0.6a Y / D () L where a is the thickness, L is the length, D is the density (mass per volume) and Y is a measure o its stiness (akin to a spring constant). The our lowest requencies are L 0.6a Y / D 6. 7, 3 7. 55, and 4 34. 39. Images rom http://www.alstad.com/barwaves/)
Clearly not integer multiples o the lowest mode. So the sound o plucking such a bar (as in a simple music box) is rather rough. Set-up (irst three steps should be done or you). Plug a unction generator into the PASCO wave driver.. With the wave driver s shat clamped into Lock position, plug the resonance strips into the end o the shat and splay the strips. 3. Un-lock the shat. Side View Top View 4. You ll observe that there are three metal strips joined by a screw such that there are six spokes o dierent lengths; you can consider each one o these spokes as an individual bar. Measure each o the six spoke s lengths rom the screw to its tip and ill in the irst column o the table below and then calculate and ill in the values or the second column (you ll use them shortly). 5. Turn on the Function Generator and set the requency to 0 Hz and the voltage to around V. 6. Set the unction generator so you can adjust the requency by 0. Hz steps. 7. Dial up the unction generator s requency until one o the beams begins oscillating strongly, when you ve adjusted the requency as to maximize the oscillation, you re driving the bar at its irst mode s requency, ; enter that into the table below. Do the same or each bar. (longest) L (m) /L (m - ) (Hz) (Hz) / (shortest) Note: don t worry about and / columns just yet, you ll be asked to come back and ill them in later. Page Physics 07 Lab #: Percussion pt.
Comparison with theory 8. Equation asserts that the requency o a bar s irst mode is proportional to /L. So, i you plot requency against this, you should get a straight line. Give it a try. 70 60 (Hz) 50 40 30 0 L (m - ) Question: Qualitatively, do they line up airly well? 9. The requency o the second mode is predicted to be 6. 7. To see those, increase the voltage to V (you may need even higher or some o them) and continue dialing up the requency and record in the table on the previous page the requencies when each bar s second mode is excited (Note, the longest beam s 3 rd mode will actually occur beore the shortest beam s nd mode; that s ine, just keep dialing up.) Then ind the ratios o these requencies or each beam and enter those into the last column o the table. 0. Calculate the average / ratio that you ve measured. / average = Question: What s the percent dierence between the average ratio you ve calculate and the predicted ratio o 6.7? Page 3 Physics 07 Lab #: Percussion pt.
Tuning ork: bars clamped together at one end Background. A tuning ork is essentially two bars anchored together at one end, so the relationship between the irst and second modes (the two you hear most strongly) is roughly the same as or a single bar, 6. 7. The exact shape o their joint can shit this ratio slightly, in act, i the base is shaped just right, then 6. 0 which is a much more musical relation. You ll see what the ratio is or our tuning orks. Set-up. Plug the Microphone into the Channel plug o the LabPro.. Open Sound Spectrum rom the Physics s older on the desktop. 3. Strike the tuning ork and record its waveorm and spectrum by pressing collect while you hold the ork near it. Note: i the irst peak is too small, try again but hold the microphone closer to the tips o the tuning ork; i the second peak is too small, try again but holding the microphone halway along the ork s length. Questions: What are the requencies o the two strongest / lowest-requency peaks? Note: i you can t see a second one, you may need to zoom out, your instructor can help you. = Hz = Hz What is their ratio? / = Is it closer to 6.0 or 6.7? Looking back at the pictures on page, observe that the tip o the bar is moved the most due to the low-requency irst mode, while the middle o the bar is moved the most due to the higher-requency second mode. Questions: So, i you strike the tuning ork and then hold it up to your ear, What part o the ork do you want to be lined up with the ear or you to hear the low-requency irst mode best? What part o the ork do you want to line up with your ear to hear the highrequency second mode best? Page 4 Physics 07 Lab #: Percussion pt.
4. Try it. Question: Were you right? P.S. You don t have to try it, but the same eect would be detectable with the microphone held near one point o the tuning ork, it would report a stronger lowrequency peak in the spectrum and held near another point it would report a stronger high-requency peak in the spectrum. Bar ree at both ends Background A bar o rectangular cross-section that s ree at both ends is the essential element o the idiophone instruments (xylophones and marimbas). The our lowest requencies are expected to be.08 a / L Y / D. 76, 3 5. 40, and 4 8. 93. The higher requencies are clearly not integer multiples o, so a struck bar doesn t sound so musical. Set-up Microphone. Close Sound Spectrum and open Sound Spectrum Trigger instead (ater you hit collect this waits or a loud sound beore it starts taking data.). You have two wooden bars, one has a uniorm rectangular cross section and the other has a scoop carved out in the middle, you ll be using the uniorm block irst pick it up by the string and let it hang so that the microphone aces the broad side o the bar, is aimed at the middle, and at least hal the bar s length away (so it s not too insensitive to modes with a node at its location.) 3. Click on collect and then strike the plain wooden bar near the bottom end o the bar so you excite all modes. This should record the sound s waveorm and Mallet spectrum. Note: I you strike the bar just in the middle and position the microphone in the middle, you can suppress the nd mode rom the recorded Page 5 Physics 07 Lab #: Percussion pt.
spectrum since it has a node there it might be un to see i you can do this, but ultimately, you want both peaks. Questions: What are the requencies o the two strongest / lowest-requency peaks? (Note: depending on how you strike the bar, you sometimes get two peaks quite near each other, i that happens, try again.) What is their ratio? = Hz = Hz / = Question: What s the percent dierence between this and the predicted ratio o.76? The two holes drilled through the bar and the act that wood is not a perectly uniorm material may be responsible or the discrepancy. 4. Beore moving on, under the menu, select store latest run ; this will keep your spectrum and wave orm so you can compare it against what you get in the next section. Marimba Bar Harmonic Modes To make the bar more musical, it can be sculpted (thinned through the middle) to make it less sti in the middle, which is where most o the lexing happens or the irst mode; thus the irst mode s requency can be lowered (while other mode s requencies would also be eected, this would be the most dramatic eect.) A marimba bar is sculpted so that 4. 0, which produces a steadier, and thus more musical tone, since is approximately a harmonic o. 5. As you did with the plain bar o wood, strike the marimba bar (the one that s scalloped on the underside) and record its waveorm and spectrum using the Sound Spectrum trigger program. Question: What are the requencies o the two strongest / lowest-requency peaks? = Hz = Hz Page 6 Physics 07 Lab #: Percussion pt.
What is their ratio? / = Question: What s the percent dierence between this and the desired ratio o 4.0? 6. Striking one and then the other bar, which (the plain bar or the marimba bar ) has a more pleasing sound? Timbre The book points out that you can change the timbre o an instrument by applying the impetus at dierent locations since modes with a node at that location will be suppressed and those with anti-nodes there will be strengthened. So, striking at dierent locations you can change the relative strength o the dierent modes and thus the timbre o the overall sound produced. Question: Following that logic, where could you strike the bar in order to suppress the second mode? 7. Try it As beore, us the microphone and LoggerPro to capture the spectrum and see how well you can suppress the second mode / diminish the second prominent peak in the spectrum. Question: Compared to when you hit the bar near its end, the overall pitch should be the same but the timbre should be noticeably dierent; was the sound s timbre brighter/colder or darker/warmer when you suppressed the second mode? Thinking o what modes (and requencies) remained prominent, explain this change in timbre. Page 7 Physics 07 Lab #: Percussion pt.