US2199120A - Sonometer - Google Patents

Description

C. J. ULRICH April so, 1940.

SONOMETER 2 sheets-sheet 1y wmyy .mmf/.m C

April 30, 1940. c. J. ULRICH 2,199,120

' SONOMETER Filed Nov. 2 1, 195e 2 sheets-sheet 2 will I lul denfior Patented Apr. 3o, 1940 UNTED STATES smear oFFi-cs SONOMETER Carl J. Ulrich, Minneapolis, Minn. Application November 21, 1938, Serial No. 241,570

8 Claims.

This invention relates to a sonometer, or in other words, to a device for illustrating or demonstrating the laws oi vibrating strings. Such instruments are commonly used in physics laboratories. It has heretofore been the practice to have sonometers constructed with a pair of strings which would be placed under tension by having weights of different sizes attached to the strings, the strings running over pulleys or to secure tension by means oi spring balances. Such devices have been cumbersome, slow and diicult to adjust and the same required a great deal or" apparatus, some of which was loose or separate from the main device.

It is an object of this invention to provide a sononieter of simple and compact form and one by means of which the laws of vibrating strings which it is desired to teach may be demonstrated without the use of weights or spring balances.

It is a further object of the invention to provide a sonometer comprising a base which is preferably in the form of a box. forming a resonator together with a pair of strings supported above said base, tensioning means at one end of said strings and a lever means at the other end of said base to which said strings are attached so that the desired relative tension can be had on said strings by lever action. y

It is another object of the invention to provide a sonometer such as above described, the same comprising scales extending between supporting members for said strings.

It is still another object of the invention to provide such a scnoineter as set forth above in which the said lever means is movable transversely oi the base and in which the tensioning means. are also preferably movable transversely of the base.

A further object of the invention is the provision or" a sonometer having a pair of strings with means for exerting different tensions thereon respectively, said strings being supported at iixed points together with a bridge movable along one or both of said strings in contact therewith and preferably together with an instrument for engaging said strings to` produce nodes therein.

These and other objects and'advantages ci the invention willbe fully set forth in the following description made in connection with the accompanying drawings in which like reference characters refer to similar parts throughout the several views and` in which- Fig. l. is a plan view of the device, some parts being broken away and others shown in horizontal section;

Fig. 2 is a view in side elevation as seen from the bottom of Fig. 1; y

Fig. 3 is a View in end elevation as seen from ther left of Fig. 2;

Fig. 1i is a view in end elevation as seen from I* the right of Fig. 2;

Fig. 5 is a transverse vertical section taken substantially on line 5-5 of Fig. l. as indicated by the arrows;

Fig. 6 is a vertical section taken substantially online 5-5 of Fig. 5 as indicated by the arrows;

7 is a vertical section taken substantially on line i-l of Fig. 8 as indicated by the arrows;

Fig. 8 is a horizontal section taken substantially on line l-- of Fig. 7 as indicated by the arrows, Figs. 5 to 8 being shown on an enlarged scale;

Fig. 9 is a top plan View of a demonstrating instrument used; f

Fig. l@ is a View in side elevation of the device shown in Fig. 9; and

Fig. ll is a perspective View of a bridge used.

Referring to the drawings a device is shown comprising a base l5. While this base could be variously formed. in the embodiment of the invention illustrated it is shown as in the form of a box rectangular in vertical and horizontal cross sectioiathe same being quite elongated and preferably having apertures` Itis cut in the sides thereof. A block lil, rectangular in vertical cross section, extends across one end oi boxV I5 adjacent the top thereof and a bracket il formed of a metal strip with its endsbent at right angles, extends along the sides of box i5 at said end and around block iii, the same being spaced somewhat from the outer side of block I6 to form a space lla. Bracket Il' is secured to box I5 and to the block i6 by the headed screws I8. A pair of tensioning devices are provided, each comprising a base plate Elia secured by screws Zlib to angle members 2l. Angle members 2| have forward portions with. vertical surfaces engaging the end ci box I5 at the top thereof and have top surfaces substantially ilush with the top surface of said box. Members 2i have downwardly extending portions 2 ia, the same extending through the space Ila and having slots 2lb cut therein in which the transverse portion of bracket Il. iits. The members 2l with the tensioning devices 2li are thus slidable transversely of box i5 at one end thereof. Said tensioning devices each also comprises a stem or shaft 20c having a flat handle portion 2M, the said stem being journaled in small upstanding brackets Zee formed` on base plate 20a. Each stem 20 porting points for the strings 22 and 23.

carries a small worm gear 20) which meshes with a small worm wheel gear 20h journaled on a small stem or shaft 201 upstanding from base plate 20a. Said worm wheel gear also has secured thereto a small cylindrical member or spool 201'. A pair of strings 22 and 23 are adapted to be connected to and wound on the spools 207' and while any suitable manner of connecting said strings to said spools might be used, in the embodiment of the invention illustrated a small cotter pin 24 extends through each spool 207' to which the ends of strings 22 and 23 respectively are secured. The tensioning devices 20 are such as commonly used on stringed musical instruments and per se form no part of the present invention. The strings 22 and 23 extend over and rest upon supporting rods 25 extending transversely of box I5 and while these rods may be of any suitable form, they are shown as cylindrical in cross section. Rods 25 are carried in blocks 23 extending transversely of and resting on the top of box I5 being secured thereto by small clip brackets 25a. Blocks 26 are secured by screws 21 to small angle brackets 28 which are in turn secured to the sides of box I5 by the screws 29. The blocks 26 are provided with undercut recesses 26a along their adjacent sides adapted to receive a pair of scale members 30, the ends of which are received in and substantially t in recesses 26a. It will be Aseen that scales 30 can readily be disposed in said recesses by having the scale extending at an angle to the side of the box and being first inserted in one recess and then being swung into the other. It will also be seen that scales 30 can be easily moved transversely of the box I 5. The scales 30 are graduated to show accurately the distance between the centers of the rods 25, or in other words, the distance between the sup- This distance in practice has been 100 centimeters, scales 30 being graduated in centimeters.

A bracket 32 having an offset central portion is secured to the end of box I5 opposite the devices 20 by suitable headed screws 33. It will thus be seen that there is a space 22a between the end of box I5 and the central portion of bracket 32. A member 34 is provided, the same having a ilange 34a disposed in space 32a, engaging the end of box I5 and having a recess 34h formed therein into which bracket 32 fits. Flange 34a extends over the top of box I5 and has a flat surface engaging said top. Member 34 has a central portion 34o extending upwardly from flange 34a, the same having formed therein a horizontal recess 34d, thus providing upper and lower arms. The member 34 is bored to receive a vertically extending pin 35 held therein by a set screw 36. Pin 35 at the portion thereof extending across recess 34d is flattened to have rearwardly converging sides 35a converging to from a knife edge at the rear of said portion. A lever 31 is provided, the same extending transversely through the recess 34d and having a triangular notch 31a formed therein embracing the triangular portion of pin 35 so that lever 31 is fulcrumed on the edge formed on pin 35. A pair of similar brackets 38 are provided, the same extending about lever 31 and being slidable thereon. While these brackets might be variously formed, in the embodiment of the invention illustrated they are shown as comprising a strip of flat metal bent around lever 31 and having their end portions in Contact and projecting somewhat at the inner side of said lever. Said brackets above the lever 31 are provided with recesses 38a through which graduations 31h formed on lever 31 may be seen. A center line 38e is marked on brackets 38 to register with the graduations on lever 31. It will be noted that lever 31 is graduated in opposite directions from a line extending to the edge of pin 35, the fulcrum point of lever 31. The inner portions of brackets 38 are provided with vertical apertures 38h substantially of circular form, the same having reduced portions extending inwardly therefrom. Each string 22 and 23 has secured thereto a hook or connector 39 adapted to be placed in the recess or opening 38h and to move into and be held in the reduced portion thereof.

A bridge 40 is provided, the same having block-like portions 40a at its bottom adapted to rest upon the top of box I5, the space between said blocks being substantially the width of the scales 30 so that said bridge ts over either one of said scales as shown in Fig. 1. Said bridge also has a portion 40h extending between and above block portions 40a, the same having one vertical side and a curved side extending away from the top of said vertical side so that said sides form an edge. Said curved surface extends downward to one side of each of the block portions 40a. A handle portion 40e is provided projecting from one end of portion 40h.

Another demonstrating instrument is provided comprising a handle portion 42 having' a bifurcated end between which is disposed a diski member 43 having convex sides meeting to form the central edge. Said disk member 42 is revoluble about a rivet pivot 42b extending between the sides of portion 42a.

In demonstrating the various laws such as the law that different tensions on strings give different tones, the strings are connected as shown as the brackets 38 will be moved so that they are the desired distances at each side of the fulcrum point of lever 31. It will be apparent that when string 22 is placed in line with numeral 2 at one side of pin 35 and the string 23 is placed in line with the numeral 4 at the other side of pin 25 and the strings are tensioned and brought to position as shown in Fig. 1 extending substantially perpendicular to lever 31, the tension on string 22 will be twice that on string 23. In other words, the tensions on the strings are inversely proportional to the distances of the strings from the pivot point of the lever.

In operation, the device can be used to demonstrate or illustrate the laws of strings. There are four of these laws, namely, the laws of length, diameter, tension and density. The law of tension is that with other factors being equal the numb-er of vibrations or the pitch of the tone produced on the string varies directly as the square root of the tension. For instance, if the tensions on the strings are as 8l to 64, the vibrations will be as 9 to 8. This can readily be shown on the instrument by setting one string 8l spaces from the fulcrum point on member 35 and the other string at 64 spaces at the opposite side of said fulcrum point. When the tension is adjusted so that the strings are substantially perpendicular to lever 31, the tensions then will be as 81 to 64. If one string is tensioned to produce the tone do then the other string will give the tone re. The relation of the vibrations of do to re is as 9 to 8. The relation of mi to do is as 5 to 4. The strings would therefore be placed 25 and 16 spaces respectively at each side of the fulcrum of lever 31. If one string gives the tone do then the other will give the tone mi. If the vibrations of one string are vtwice those of the other then the tone on one string will be an octave higher than the tone on the other. This can readily be seen on the instrument by placing one string four times the distance from the fulcrum as the other. The law of tension can thus be very easily and conveniently demonstrated on the instrument. It does not matter what the aboslutetension is. In former soncmeters it was necessary to get the difference in tensions either by the use oi' Weights or -by the use of spring balances. This necessitated numerous weights and several sets of spring balances. Even then, very few different tensions could be secured for proper demonstration. With the present device the diiierent de grecs of tension are almost unlimited.

The law of length is that with other factors equal the number of vibrations varies inversely as the length. If the string is half the length of `another it will give a tone an octave higher. It will be seen that this law oi length may be easily .and quickly demonstrated by the use of the bridge 40. This bridge can be Ymoved along either one of the scales 30 so that the string can be divided as desired. The lengths required to obtain the various tones D, E, F, G, A, B and high C can be -determined by moving the bridge and using the other string as a check on the original C.

The law of diameters is that with all other factors equal the vibrations will be inversely as the diameters. Thus if the diameter of one string is twice the diameter of the other the strings can be set at equal distances at opposite sides of the lever fulcrum and the string will have twice the vibrations of the other or will give a tone an octave higher. If the diameters are as 16 to 24 or as 2 to 3, the vibrations will be as 3 to 2 so that if one string is tuned to give the note do, the other will then give the note sol. Using one number 3 string (Malins music wire number (3.624) and one number 10 string, which latter string is twicethe diameter of the former, the strings can be spaced equallyfrom the lever fulcrum and the number 3 string tuned to give the tone C. The other string will then give upper C or a tone just an octave higher.

The law of density is that the number of vibrations varies inversely as the square root of the density the length and tension being the same. Thus if the densities are as 4 to l the strings could be set respectively equal distances at either side of the lever fulcrum and the lighter string would then give a tone an octave higher than the other.

The device is also particularly adapted to illustrate overtones or harmonics. The instrument 42 is then used. The disk 43 is preferably made of fairly hard rubber. The material in this instrument is important. If hard cardboard, paper, hard Wood or ber is used a rattling effect is produced on the tones. By vibrating one of the strings and then placing the edge of disk 43 at some point thereon, the overtone can be distinctly heard. The rst overtone is formed when the string vibrates in halves. This overtone is thus one octave higher than the fundamental tone. The second overtone is when the string vibrates in thirds and the overtone is the fifth tone in the octave above the fundamental tone. This can be nicely demonstrated by placing the edge of disk d3 at one-third the length of one of the strings. the string vibrates in fourths, in fthsand sixths, can be nicely demonstrated. Said overtones The other overtones as whenr produce notes in the scale and thus produce harmonics. The sixth overtone is produced when the string vibrates in sevenths or in seven sections. The tone produced by the overtone in this case is not a tone in the scale and is not a harmonic. If the edge of the vdisk Q3 be placed at one-fourth the distance from the end of one string and thestring lis then plucked to cause vibration at one-fourth the distance from its other end, a vblunt tone will be produced. The string attem ,ts to vibrate in fourths but the plucking at the said point produces the widest vibrations where there should be substantially no vibration. The overtone vibrations or nodes are thus intrfered with and the blunt tone results. This can be nicely shown with the device. Regular music wires can be conveniently used on the device. Malinsmusic wire number 3 has a diameter of 0.012 inch and can stand a tension when the full i@ centimeters provided on the device for length is used sufcient to give the tone C or 256 vibra- `tions per second. Number l0 wire with 0.024

inch in diameter can stand a tension when the full string length is used to give the tone G or 192 vibrations per second.

It willthus be seen that the device can be `used in many ways to illustrate the laws of strings. The `device is simple and compact and the relative tensions of the string are obtained with great ease by merely making the proper adjustments on lever 31. It will be seen that the strings can be very quickly and easily removed by merely lifting small hooks or clevises 39 from the brackets 33 and by merely withdrawing the cotter pins- 34. The strings are preferably connected to the eyelet end of the cotter pins and then disposed so as yto wind on the spools 207'. The rods 25 in practice have been made of glass.

From the above description it will be seen that I have provided a novel, simple, compact and muchimproved construction of sonometer. The

same has been amply demonstrated in actual practice and is being commercially made.v

It will, of course, be understood that various changes may be made in the form, details, arrangement and proportions of the parts,`without departing from the scope of applicants invention, which generally stated, consists in a device capable of carrying out the objects above set forth, in the parts and combinations of parts disclosed and dened in the appended claims.

What is claimed is:

i. A sonometer having in combination, a base, a pair of strings supported above said base, means at one end of said strings to which said strings are attached to have tension exerted thereon and a lever means at the other end of said strings arranged to swing about a fulcrum axis extending substantially perpendicular to said base With said strings at dierent distances from said fulcrum point so that the tension on said strings will be proportional to the distances of said strings from said fulcrum point. v 2. A sonometer having in combination, a base, a pair of strings supported above said base, supports extending transversely of said base adjacent the ends of said strings, means/at one end of said strings for exerting tension thereon, a lever at the other end of said base, means for movably attaching the other ends of said strings to said lever so lthat they can be positioned at different distances from the fulcrum of said lever whereby the tension on said strings will be proportional to the distances of the same from said fulcrum respectively.

3. A sonometer having in combination, a base in the form of a box forming a resonator, a pair of strings above said base extending longitudinally thereof, means for exerting tension upon one end of said strings respectively, a member movable transversely of said base at the opposite end thereof, a lever carried by and fulcrumed on said member about an axis substantially perpendicular to said base and means for attaching the other ends of said string respectively movably to said lever.

4. A sonometer having in combination, a base in the form of a box forming a resonator, a pair of strings supported above said base and extending longitudinally thereof, means at one end of said strings for exerting tension thereon, a lever at the other end of said base to which said strings are movably connected, the axis about which said lever moves being substantially perpendicular to the top of said box, means over which said strings pass and with which they contact adjacent each end of said base and a scale for each of said strings extending between said last mentioned members.

5. The structure set forth in claim 4 and members extending transversely of said base beneath said strings having recesses in their adjacent sides into which the ends of said scales extend.

6. The structure set forth in claim 4 and a bridge member insertable under one of said strings for engaging the same, said bridge meme ber being movable longitudinally of said base and string.

7. A sonometer having in combination, a base, a pair of strings supported above said base and extending longitudinally thereof, a pair of brack.- ets at one end of said base movable transversely thereof, means on each of said brackets for exerting tension on said strings to which said strings are respectively connected, a lever at the opposite end of said base and means for detachably and movably connecting the other ends of said strings to said lever.

8. A sonorneter having in combination, a base, a pair of strings supported above said base and extending longitudinally thereof, means secured CARL J. ULRICH.

Images