EXPERIMENT - NCERT

1 EXPERIMENTEXPERIMENTEXPERIMENTEXPERIMENT EXPERIMENTAIMTo determine the frequency of alternating current using a sonometerand an AND MATERIAL REQUIREDA sonometer with a soft iron wire stretched over it, an electromagnet,a step-down transformer, slotted 1/2 kg weights hanger, a physicalbalance, two sharp edge wedges and a weight frequency n of the fundamental mode of vibration of a stretchedstring, fixed at two ends, is given by12 Tnl m=Here l is the length of the vibrating string, T is the tension in the wireand m is its mass per unit an alternating current is passed in the coil of the electromagnet, themagnetisation produced in the core is proportional to instantaneousvalue of the current. If the electromagnet is held close to the middle ofthe sonometer wire, the wire will be attracted twice during each cycletowards the electromagnet.

2 The attractive force experienced by thewire will be proportional to the magnetisation produced in the core ofthe electromagnet. Since in each cycle, the wire will be pulled twiceand hence at resonance, it will vibrate with a frequency which is twicethe frequency of alternating current. Hence, if f is the frequency of thealternating current, then124nTfl m==4n2 l 2 m = T88888(E )(E )24/04/201866 LABORATORY MANUALor2214lTn m= A graph between T (taken on x-axis), and l 2 (taken on y-axis), wouldbe a straight line. The slope of this straight line would be142n m, so thatnm slope214= nm slope= 121 The frequency of alternating current, fnm== 2141slope can bedetermined using the value of the up the sonometer and stretchthe wire AB by placing a load of kg on the hanger (Fig.)

3 E ). the electromagnet ina stand and connect it tothe secondary of a stepdowntransformer. Adjust its position,such that its one pole lies closeto the middle of the sonometer on the alternating currentsupply and adjust the length ofvibrating portion of AB by sliding thewedge W or W . Make this adjustmentuntil the amplitude of the vibratingstring is the vibrating length andnote the tension in the the load in steps of kg andeach time find the vibrating off the ac supply. Untie thewire of the sonometer from its peg and find its mass in a physicalbalance. Calculate mass of 100 cm sonometer wire. Hence findthe mass per unit length, m for the E up for finding frequency of ac mainsusing a sonometer(E ) of the wire =.

4 Cm = .. of the wire = ..g = .. per unit length, m = .. g/cm = .. due to gravity, g = .. each set, calculate the value of n using the formula givenabove. Find the mean of these a graph of l 2 against T with l 2 on y-axis and T on the slope of the graph. Using the value of the slopedetermine the frequency of alternating graph between T and l 2 is a straight of the graph = mn214 = .. of ac supply f = 2n(i)from calculation ..Hz(ii)from graph ..Hz8 Table E : Resonant (M)includingmass ofhanger(kg)Ten-sionT = mg(N)Resonant length lFirsttrial(cm)Secondtrial(cm)Mean(cm)Me an lin(m)12=Tnl m(Hz)Mean24/04/201868 LABORATORY should be as frictionless as of the wedge should be of the electromagnetic pole should be close to the middle of thesonometer taking each of the observations, circuit should be switchedoff for a few OF of the pulley is the main source of error in the to this, the value of tension acting on the wire is less than thatactually frequency may not be frequency of alternating current is half that of the frequency ofthe vibrating wire is made of soft iron for better is ac different from dc?

5 Is the meaning of frequency of ac? does the wire vibrate? Identify and explain the rule with thehelp of which you can determine the direction of force acting onthe should be the property of the iron for making it agood electromagnet? there any relation between frequency and magnetism of theelectromagnet, and frequency of the alternating current?SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIESP erform the above EXPERIMENT using a permanent horse shoe magnet and passingthe alternating current in the sonometer wire. In this case the resonant frequencyis equal to the frequency of the alternating current. Sonometer wire need not bemade of soft iron. You can use constantan or manganin wire for this find the value of v for different values of u in case of concavemirror and to find the focal AND MATERIAL REQUIREDAn optical bench, two sharp-edged needles (pins), concavemirror of less than 20 cm focal length, three uprights (withclamps), index needle (may be a knitting needle), metre scaleand spirit AND axis of a mirror is the linepassing through the centre ofcurvature and pole of the focus is the point whererays parallel to principal axis, focusafter reflection from the surface ofthe mirror (Fig.)

6 E ). centre of the mirror iscalled pole, length is the distance betweenthe pole, P and the focus, CORRECTIONU sually the distance between concerned points of two elements isnot the same as the distance between their uprights as read onthe scale. For example, in Fig. E the reading of two uprightsdo not give the actual distance between the tip of the pin and thepole of the mirror. A correction must, therefore, be applied. It iscalled the index E Focal length of a concave MANUALPARALLAXThis is employed in the locationof image of an example, as shown in theFig. E (a) O and I are theobject and image points for object point O and its realimage I are conjugate points of the two may be consideredas object and the other as itsimage.

7 Thus it helps in accurateadjustment to check for noparallax at both the we say there is no parallaxbetween an object O (pin) and itsimage I, then by moving the eyethrough which we are observing,to the left and then to the right,object and its image both appearto move together relative to thelens/mirror. It implies that theposition of both are same on theoptical bench [Figs. E (d) and(e)]. If their positions are not samethen in one position they mayappear to coincide and in anotherthey will appear separate [Figs. (b) and (c)].This method of locating theposition of an image on the opticalbench by a pin is called themethod of E (a),(b),(c)Locating the position of an imageon the optical bench by a pinFig.

8 E Determination of Index correction(a)(b)(c)24/04/201871 EXPERIMENTSIGN the distances are measured from the pole P of the mirror (orthe optical centre of a lens). distance measured in the direction of propagation of incidentrays are taken as positive and those measured in the oppositedirection are taken heights measuredupwards (above theprincipal axis ofthe mirror/lens) aretaken as positive andthe heights measureddownwards are takenas negative (Fig. E ).Note: In the cartesian signconvention, the object isalways placed to the left ofthe mirror (or the lens).Fig. E The cartesian sign convention9(d)(e)Fig. E (d), (e) Ray diagram for finding focal length of a concave mirror24/04/201872 LABORATORY MANUALRAY TRACING IN SPHERICAL MIRRORSTo locate the image, we need to trace only afew specific paths or rays (a minimum of two)as shown in Fig.

9 E , any two rays can be taken tolocate the incident ray parallel to the principalaxis of the mirror either passes throughthe principal focus F (concave mirror)or appears to be diverging from it(convex mirror). incident ray passing through thecentre of curvature C (concave mirror)or appearing to pass through it (convexmirror), retraces its path reflectedback along its original path. You must note that this ray isincident normal to the incident ray passing through the principal focus F (concavemirror) or appearing to pass through it (convex mirror) will bereflected from the mirror parallel to the principal incident ray striking the pole P of the mirror is reflected atan angle equal to the angle of incidence with the principal an object placed at a distance u from thepole of a concave mirror of focal length f, theimage is formed at a distance v from the relation between these distances (for aconcave mirror) is 11 1fu v= +or uvfu v=+If an object (say, a pin)

10 Is placed in front of thereflecting surface of the concave mirror suchthat the object s position lies in between theprincipal focus of the mirror, F and the centreof curvature C, then a real, inverted andmagnified image is formed in between the centre of curvature C of themirror and infinity (Fig. E ).Fig. E tracing for image formationby a concave mirrorFig. E Formation of image by a concave is between the centre of curva-ture and principal focus F; real, invertedand magnified image is between thecentre of curvature and infinity24/04/201873 EXPERIMENTThus, the image formed in such a case would be clearer and easier tobe seen. The focal length of the mirror, using the above relation, can bedetermined by placing the object in between the point 2F and focus approximate value of the focal length of concave mirrorby focusing the image of a distant object.