5. In a location where the speed of sound is 354 m/s, a 2 000-Hz sound wave impinges on two slits 30.0 cm apart. (a) At what angle is the first maximum located? (b) If the sound wave is replaced by 3.00-cm micro- waves, what slit separation gives the same angle for the first maximum? (c) If the slit separation is 1.00 µm, what frequency of light gives the same first maximum angle?

5. In a location where the speed of sound is 354 m/s, a 2 000-Hz sound wave impinges on two slits 30.0 cm apart. (a) At what angle is the first maximum located? (b) If the sound wave is replaced by 3.00-cm micro- waves, what slit separation gives the same angle for the first maximum? (c) If the slit separation is 1.00 µm, what frequency of light gives the same first maximum angle?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter3: Interference

Section: Chapter Questions

Problem 62AP: An effect analogous to two-slit interference can occur with sound waves, instead of light. In an...

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Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where sin, with in radians), the distance between fringes is given by y=x/d. Figure 27.56 The distance between adjacent fringes is y=x/d, assuming the slit separation d is large compared with .
A 5.08-cm-long rectangular glass chamber is inserted into one arm of a Michelson interferometer using a 633-nm light source. This chamber is initially filled with air (n=1.000293) at standard atmospheric pressure but the air is gradually pumped out using a vacuum pump until a near perfect vacuum is achieved. How many fringes are observed moving by during the transition?
A Michelson interferometer with a He-Ne laser light source (=632.8nm) projects its interference pattern on a screen. If the movable mirror is caused to move by 8.54 m , how many fringes will be observed shifting through a reference point on a screen?
Young’s double-slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.
Calculate the wavelength of light that produces its first minimum at an angle of 36.9° when falling on a single slit of width 1.00 m.
Check Your Understanding For the experiment described in Example 4.7, what are the two other angles where interference maxima may be observed? What limits the number of maxima?
An effect analogous to two-slit interference can occur with sound waves, instead of light. In an open field, two speakers placed 1.30 m apart are powered by a single-function generator producing sine waves at 1200-Hz frequency. A student walks along a line 12.5 m away and parallel to the line between the speakers. She hears an alternating pattern of loud and quiet, due to constructive and destructive interference. What is (a) the wavelength of this sound and (b) the distance between the central maximum and the first maximum (loud) position along this line?
If 500-nm and 650-nm light illuminates two slits that are separated by 0.50 mm, how far apart are the second-order maxima for these two wavelengths on a screen 2.0 m away?
In a thermally stabilized lab, a Michelson interferometer is used to monitor the temperature to ensure it stays constant. The movable mirror is mounted on the end of a 1.00-m-long aluminum rod, held fixed at the other end. The light source is a He Ne laser, =632.8 nm . The resolution of this apparatus corresponds to the temperature difference when a change of just one fringe is observed. What is this temperature difference?
What is the wavelength of light falling on double slits separated by 2.00 m if the third-order maximum is at an angle of 60.0° ?
If a hologram is recorded using monochromatic light at one wavelength but its image is viewed at another wavelength, say 10% shorter, what will you see? What if it is viewed using light of exactly half the original wavelength?
Check Your Understanding Although m, the number of fringes observed, is an integer, which is often regarded as having zero uncertainty, in practical terms, it is all too easy to lose track when counting fringes. In Example 3.6, if you estimate that you might have missed as many as five fringes when you reported m=122 fringes, (a) is the value for the index of refraction worked out in Example 3.6 too large or too small? (b) By how much?