The wavevelocity of the wave in the string can also be determined from a fit to thedata.įigure 3 Graph of fundamental freqency vs. 3 below, thefit is extremely close to the theoretical 1/L dependence given in the equation. Whilethis entails re-doing that data point so that the frequency of the fundamentalnote is shown on the digital meter, the entire data collection is fast enoughthat this has not been a significant problem for my students or me.īy varying the location ofthe bridge, the dependence of the fundamental frequency of a wave on a stringas a function of length can be experimentally determined. 2 the fundamental frequency as dominant, I shouldnote that sometime the second or third harmonic is the highest intensity noteand recorded as dominant. I have found that it helps to place a finger on the far(unplucked) side of the bridge to dampen any unwanted rattles and for onepartner to hit the “freeze” button as soon as he/she sees the second personpluck the string (the response time matches well with the ending of the“attack”). With the cheap equipment and noisyenvironment that I have, the data collection is slightly finicky, but mystudents quickly learn to recognize “good” data. In order to determine the fundamental, the students simplypluck the string while watching the tuner on the screen. In the spectrum “A smallred cross is drawn on the top of the line relevant to the dominant frequency.” The freeze/thaw spectrum key temporarilyfreezes all meters and allows the student to study the transient sound. As can be seen below, the screen showsthe spectrum, a digital frequency meter and the nearest note on a musicalstaff. This program, designed as a guitartuner, is easy to use and explicitly free for academic use. On the PC is a sharewareprogram named wtune. Not shown in the schematic is the input microphone andPC. Thestrings do have a slight tendency to dig into the fairlead, but this can beeasily compensated for by picking up and replacing the string whenever thetension is changed. Also to conserve money, instead of using pulleys theweighted end of the string is run over a fairlead made of two short pieces ofPVC pipe glued together. To conserve money, the weights are simply small sandbags or 1- and 2-Lbottles of water (1 L of water masses 1 kg). The far endof the string has be twisted and soldered into a loop to hold an “s”-hook, fromwhich calibrated weights are hung. A second piece of Al angle stock isused as a bridge and determines the relevant length of the string. When using guitar strings, the ferrule of the guitar stringis held in a small slit in the bottom of a short piece of aluminum angle stockand wrapped over the top of this piece. I have alsosuccessfully used ice-fishing line, which gives good results with lesstension. Not only are they convenient and cheap,but they sound pleasant and the students have a sense what sounds are“correct”. I usually use standard guitar strings as the string. Additionally, the tuner program clearly shows the harmonic modes of thestrings. Data taken with this sonometer clearly showthe inverse dependence on length and the square root dependence on stringtension of the fundamental frequency. Assuming a PC is already available to the students, a sonometer canbe constructed for approximately $. Plans for an inexpensive and enjoyable student sonometer arepresented.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |