12. PRELAB FOR INTERFERENCE LAB
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1 12. PRELAB FOR INTERFERENCE LAB 1. INTRODUCTION As you have seen in your studies of standing waves, a wave and its reflection can add together constructively (peak meets peak, giving large amplitude) or destructively (peak meets valley, canceling each other). This type of adding is called INTERFERENCE, and it depends on the relative phase of the interfering waves. Since the direct and reflected waves are coming from the same source, they clearly start out in phase. Whether or not they come back together in phase depends on path length. If the difference in the two path lengths is 1,2,3,etc. wavelengths, then the waves will be back in phase. If there is an extra ½ wavelength, however, they will be out of phase. 2. AN EXAMPLE OF MICROPHONE PLACEMENT The next page contains an excerpt from an article on the importance of a microphone placement. Read the excerpt and answer the following questions: 1. When the pressure wave is reflected from the table, is there a 180 o phase shift? (Think back to the standing waves in the open and closed tubes). 2. Look at Fig from the excerpt. Suppose that the direct sound travels 2 meters, and the reflected sound covers a greater distance of 2 ½ meters. Therefore, the difference in the two path lengths is d = 0.5m. Constructive interference will occur when d = λ, 2λ, 3λ, 4λ,, where λ is the wavelength. Use the relation v = λ f, (v speed of sound, f frequency) to calculate the first four frequencies at which constructive interference will occur. Assume v = 344 m/s. Then, calculate the first four frequencies at which destructive interference (d = ½ λ, (1+½) λ, (2+½)λ, ) will occur. Constructive interference Destructive interference 1. f 1 (constr) = Hz f 1(destruct) = Hz 2. f 2 (constr) = Hz f 2(destruct) = Hz 3. f 3 (constr) = Hz f 3(destruct) = Hz 4. f 4 (constr) = Hz f 4(destruct) = Hz 12: Interference Lab - 1
2 12: Interference Lab - 2
3 3. INTERFERENCE PATTERNS IN SPACE Pressure pulses travel out from a sound source in concentric spheres. When two closely spaced, identical sources emit sounds, an interference pattern of loud and soft is produced. 1. The next page shows such an interference pattern. The lines drawn through the crossing points of the circles show the loud areas. 2. The page after that is blank. Use a COMPASS to make an interference pattern like the example, except with the sources closer together, as shown. The scale at the bottom of the the page shows the spacing of the circles of high pressure. Draw lines through the crossing points to show the loud regions. Mark with dotted lines the soft regions. 3. Use another blank page to make a drawing assuming the same source separation as before, and twice longer wavelength. 4. Compare cases 1, 2 and 3. Write down your observations. 12: Interference Lab - 3
4 An example of interference pattern 12: Interference Lab - 4
5 Prelab assignment: Draw an interference pattern for the given speakers separation and the same wavelength as on previous page. Either use the same drawing, or a separate blank page to see the effect of doubling the wavelength. 12: Interference Lab - 5
6 12A. INTERFERENCE LAB ACTIVITIES 0. DEMONSTRATIONS We will start this lab with two demonstrations illustrating your prelab analysis. a. Interference and microphone placement demonstration. b. Water waves in a Ripple tank. 1. STANDING IN A RIPPLE TANK OF SOUND This is an outdoor activity. Two loudspeakers will be mounted in the room windows pointing toward the 3 rd Street. They will be driven by a Function generator set to a sine wave of 400 Hz. This frequency, coupled with the speed of sound of 344 m/s corresponds to the sound wavelength of λ = 344 m/s / 400 Hz = 0.86m. The speakers will be approximately 1.2m apart. The sound from the two speakers will form an interference pattern analogous to the one discussed in your prelab and shown for water waves. To observe this pattern the students will assemble on the sidewalk outside the building. They are asked to walk back and forth along the sidewalk finding the loud and soft places. 1.1 Straight Lines with Maximum or Minimum Sound Find the position of central maximum. Students should form a line going out toward 3 rd Street along the central maximum, as shown in the figure. 12: Interference Lab - 6
7 Next, each student should walk East, until he/she finds the first minimum of sound. Stop there. The students should again be forming a straight line pointing to the place between the two speakers. If you continue, you should find the first secondary maximum. Again, students are expected to form a straight line pointing at the center. Find positions of at least the first TWO minima and ONE secondary maximum. Repeat the measurements walking West from the central maximum. Positions of minima and maxima either to the East or to the West are expected to be symmetric with respect to the central axis. 1.2 Data recording Using a measuring tape, find (one measurement for all students): - separation between speakers, D = - distance from the building to the far edge of the sidewalk, L = - positions of minima along the far edge of the sidewalk, with respect to the central maximum: dmin 1 =, dmin 2 = - - position of the secondary maximum along the far edge of the sidewalk, with respect to the central maximum: dmax 1 = 1.3 Data analysis (to be completed once you are back in the building). Using the measured values of D and L and the known wavelength λ = 0.86 m, predict values of dmin 1, dmin 2, and dmax 1. There are two methods you can use to predict positions of the minima: (a) a graphic method, i.e. draw an interference pattern with proper scale for the speakers separation and the wavelength. (b) use the formula for angles θ i at which minima should be observed: sin (θ i ) = (i-½) λ / D, where i is an integer number. Then, calculate dmin 1, dmin 2 from the formula: dmin i = L tan ( θ i ). Compare your predictions with the measured values. Do they agree? (c) use the formula for angles θ i at which maxima should be observed: 12: Interference Lab - 7
8 sin (θ i ) = i λ / D, where i is an integer number. Then, calculate dmax 1 from the formula: dmax 1 = L tan ( θ i ). Compare your predictions with the measured values. Do they agree? 1.4 Observing Beats in Space (optional) Beats in space are caused by a moving interference pattern. If the two speakers are driven from two function generators, with slightly different frequencies, the interference pattern no longer will be stable and the beats will be heard. However, if one synchronizes his/her motion with that of the interference pattern, he/she may either not hear beats or hear them with different frequency. The students are encouraged to jog back and forth along the sidewalk, speeding up or stopping the beats. 12: Interference Lab - 8
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Outer Diameter 23 φ mm Face side Dimension 20.1 φ mm. Baffle Opening. Normal 0.5 Watts Maximum 1.0 Watts Sine Wave.
1. MODEL: 23CR08FH-50ND 2 Dimension & Weight Outer Diameter 23 φ mm Face side Dimension 20.1 φ mm Baffle Opening 20.1 φ mm Height Refer to drawing Weight 4.0Grams 3 Magnet Materials Rare Earth Size φ 9.5