Physics Chemistry-Biology Technics S. 7/1989-Si- LEYBOLD LEYBOLD DIDACTIC GMBH Instruction Sheet 401 03 (4j) Vibrating Thread Apparatus The vibrating thread apparatus car» produce standing transverse waves of circular polarization. The frequency f*of the waves remains constant but the wavelength X can be altered. The wavelength changes with the specific mass m* (mass per length) of the thread and with the tension F applied to the thread. This force F is measured by a spring balance tied to v one end of the thread. This compact arrangement allows for an easy demonstration of Melde's experiment showing the velocity of propagation c (phase velocity) of transverse waves along cords under tension: (l)*5 c "l/fTT for homogeneous materials (for example wires) of the dssstty-p and the cross section A ■v? os c ~\j~ for inhomogeneous materials (for example stranded threads) with m* being the specific mass Results obtainable with this apparatus: The wavelength of a cord subjected to the forcef is half that of a cord subjected to 4 x /% The wavelength of a cord with the mass m * is twice that of a cord having four times that mass m* under the same force. Thus the proportionality fr ... m* is verified. Using the equation c - X- f it follows that ÍF X *» wavelength f ■ frequency c = velocity of propagation Further possible experiments: Experimental derivation of c ~ y F by quantitative examination of the relation between F and X for a number of X Values; evaluation of the propagational velocity c according to (I). Comparison of the value of c obtained according to method (I) and the value calculated from the equation c = X- f (stroboscop-ic measurement off). This apparatus also allows for a comparison between circular and linear polarized waves. The influence of a polarizer on the rotating plane of oscillation of a circularly polarized wave can also be demonstrated. ..... --s mmťh ■ ■;■ ■ ■ . .-;■ ^ Fig, 1 Literaturo: Physics Experiments, Volume 2 (599:922) New Physics Leaflets lor Colleges and ' 'niveryt'ies, Volume 1 (599952) 1. Technical Data Effective lengths / of the thread for standing Waves approx. 0.485 m or approx. 0.38 m approx. 5; mg/cm range max. ÍM Specific mass m* of the thread Tension as shown on the spring balance Excitation of the thread by an eccentric of a drive motor Power supply voltage: 220 V/50 Hz Rated power: approx. 23 VA Frequency: approx. 44 Hz. Dimensions (excluding the vertically 'adjustable holder; max. height 55 cm) approx. 70 cm x 15 cm x 14 cm Weight: approx. 2,5 kg +l Eq. 1 follows from the solution of the wave equation of cords and threads under tension, neglacting bend; .'3 strength, The derivation may be found in theoretical physici books. _____^^__ Description l\k Parts included in standard specification complete with basic apparatus (motor, housing and base), inkier, vertically adjustable to be mounted on the base, 1 spring balance {range í NJ* approx. 5 m Of thread. 0 Basic apparatus with motor © Mains switch with indicator lamp 0 Mains cable © Excenter © Vertically adjustable holder for the spring balance © © Spring balance, 1 N 0 Screw to fix the heigth of © © Guide roller for near frictipnless transmission of the force to the horizontally mounted thread © and ® Bores for the holder © ® Hexagonal nut, butterfly nut and washers for mounting the holder © onto the base of © @ Approx. 5 m of thread .for making threads of various masses and lengths. (See 3.1,) 2.2. Principle of Operation The excenter of the motor producesa circular movementof the thread end whereby the frequency f of the motor remains nearly constant under any load for these experiments. This periodical dislocation moves along the thread with the propagation velocity c so that a circularly polarized wave is produced. This wave is reflected off the guide roller with a phase shift •because the guide roller acts as a fixed end. As the arriving wave interferes with the reflected wave a standing wave appears when the following conditions are met; The wavelength X as given by the force F and the specific mass m* must be so that just a multiple integer of— can be accommodated along the thread. 3. Operation 3.1. Preoperation measures (usually only required before initial operation) Prepare the necessary threads for the experiments according to F ig. 3. (a)- m=1 (b), m = 4 (c)-or- m»4 -S&. m=1 (d)-= P'9.3 m=1 Thread (a): Thread (b); Thread (c): Approx. 0.6 m of thread is needed; effective length / m 0.485 m. single mass m; to verify: X ~ T/JF* Approx. 2.40 m of thread is needed-effective length / = Q.-483 m; four times the mass» Am used with thread (a) to verify: "m ingle X~l/-i-( Approx. 1,35 m of thread is needed; effective length / m 0.485; oné half is of the single mass m, the other half is of four tin,-.s the single mass 4 m used to verify: X ~ y—•, Thread (d): Approx. 0.50 m of thread is needed; effective length / * 0.38 m; single mass m; used together with thread (a) to derive X ~ 1/K? Mount the adjustable holder on to the basic apparatus by inserting it into the bores in the base using the hexagonal nut, the two washers and the butterfly hut äs shown in Fig, 2, Hint For the experiments it is sufficient to generate waves of X - 0.48 m and 0.32 m. This can be done by mourting the adjustable holder at bore © giving an effective length of 0.48 m. When making a graph of the function X = f \F) it is advisable to make additional measurements with a thread having a length of 0,38 m in order to obtain different X-values. To do this the adjustable holder may be mounted on the bas« using; bore @, 3.2. General hints for experimenting The apparatus is ready for the experiments When the spring balance and a suitable thread (see 3.1.) are set up as shown in Fig. 1 and after having connected the motor to the mains. When relaxing the screw © the height of the holder should be varied slowly and continuously whilst observing the thread until standing waves appear with their maximum amplitude. Then tighten the screw and note the force as shown ! ■/ the spring balance. Tensions above 0,7 N impair the frequency of the motor. - / \ s Specific mass/7}* *0.52 x 10-3 kg/m (calculated from weigh-ii^ 0.6 m óf thread) 1 Mfrom 1.1; 1,2) m 0.76 0.485 0.38 0.323 0.253 0.194 F(fromT.1;1.2) N 0.58 054 0.15 0.1 0.07 0.04 \2 m2 0.S78 0.24 0.14 0.104 0.064 0.038 II "M 314 21.48 1658 13.87 11.6 8.77 111 f i 44.6 44.8 44.8 44.6 44.7 445 e-X-f £2. s 33.9 21.73 17.02 14.41 11.31 8.69 Table 2 Hold the polarizer (either a piece of bent wir« or a piece Of cardboard with a slit) as shown in Fig. 8 and turn it slowly as indicated by the arrows. (Illumination by the stroboscope 451 28 is advisable); observe the plane of oscillation before and after the v aye has passed the polarizer. LÉYBOLD DIDACTICGM8H • Leyboldstraße 1 • 0-50354 Hürth- Telefon (02233) 604-0 • Telefax (02233) 604-222 - Telex 17 223 332 LHPCGN D