Section 9.3: Diffraction and Interference of Water Waves Tutorial 1 Practice, page Given: λ = 1.0 m; w = 0.5 m

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1 Section 9.3: Diffraction and Interference of Water Waves Tutorial Practice, page 46. Given:.0 m; 0.5 m Required: Analysis: Diffraction should be noticeable if, so solve for..0 m 0.5 m Statement: Yes, the diffraction should be noticeable because is greater than.. Given:! 630 nm m Required: maximum idth for noticeable diffraction Analysis: Use the condition that.! "! " 6.3 # 0 $7 m " Statement: The maximum slit idth for significant diffraction to be produced is m. Mini Investigation: Interference from To Speakers, page 464 A. Ansers may vary. Sample anser: The distances to the to speakers should differ by zero or a hole number of avelengths to get constructive interference. B. Ansers may vary. Sample ansers: The distances to the to speakers should differ by a half-hole number of avelengths to get destructive interference. C. Ansers may vary. Sample ansers: If a sound of knon frequency and avelength is played, students can compare their estimates ith the knon values. Tutorial Practice, page 468. Given: to-source interference;.5 m Required: d, smallest path difference for a node Analysis: Use n ith n. n n Copyright 0 Nelson Education Ltd. Chapter 9: Waves and Light 9.3-

2 n n (.5 m). m Statement: The smallest path difference for a node is. m.. (a) Given: n 3; P3S 35 cm; P3S 4 cm Required: Analysis: n n n cm 4 cm.5.8 cm Statement: The avelength of the aves is.8 cm. (b) Given: f 0.5 Hz;.8 cm Required: v Analysis: v f v f (0.5 Hz)(.8 cm) v 9 cm/s Statement: The speed of the aves is 9 cm/s. 3. (a) Given: n ; PS 9.5 cm; PS 5.0 cm; v 7.5 cm/s Required: Analysis: n n n Copyright 0 Nelson Education Ltd. Chapter 9: Waves and Light 9.3-

3 9.5 cm 5.0 cm cm Statement: The avelength of the aves is 3.0 cm. (b) Given: v 7.5 cm/s; 3.0 cm Required: f Analysis: v f v f v f cm 7.5 s 3.0 cm f.5 Hz Statement: The frequency at hich the sources are vibrating is.5 Hz. Section 9.3 Questions, page 469. Diffraction of aves through a slit is maximized hen the avelength is comparable to or somehat greater than the slit idth.. Ansers may vary. Sample anser: When the aves reach my friend in phase, there is constructive interference and he hears a loud sound. When the phase of one speaker is changed by 80, the aves reach my friend out of phase and he hears a sound ith decreased volume (a) Given: m Required: maximum idth for noticeable diffraction Analysis: Use the condition that m Statement: The maximum slit idth for noticeable diffraction is m. (b) Sample anser: If the slit is ider than m, there may still be some diffraction. The ider the slit is, the less diffraction ill be noticeable. Copyright 0 Nelson Education Ltd. Chapter 9: Waves and Light 9.3-3

4 4. Given: d.0 m; 0.5 m; n Required: θ Analysis: dsinθn n n sinθ n d # n " & $ % sin! n ' ( ) d # # " & & % $ %! sin " ' ( (0.5 m) ( % ( $.0 m '! 7. Statement: The angle of the first nodal line is Sample anser: For the interference pattern from a to-point source to be stable, the phase beteen the sources must not change. 6. (a) (b) Given: d 5.0 cm; n ; x 45 cm 35 cm 0 cm; L 50 cm; f 6.0 Hz Required: Analysis: The distance from the nodal points to the midpoint beteen the sources is close to the L distance L beteen the line joining the sources and the metre stick. Rearrange xn n d xd n to determine the avelength,. n L Copyright 0 Nelson Education Ltd. Chapter 9: Waves and Light 9.3-4

5 xd n n L (0 cm)(5.0 cm ) (50 cm ) cm Statement: The avelength of the aves is cm. (c) Given: cm; f 6.0 Hz Required: v Analysis: v f v f (6.0 Hz)( cm) v cm/s Statement: The speed of the aves is cm/s. 7. (a) Given: n 3; x3 35 cm; L 77 cm; d 6.0 cm; θ3 5 ; distance beteen 5 crests 4. cm Required: Calculate using three different methods. L Analysis: For the first method, use xn n, ith n 3. For the second method, use d dsinθn, ith n 3. For the third method, use the measurement beteen ave crests to determine the avelength directly. First method: L xn n d xd 3 3 L (35 cm)(6.0 cm ) 3 (77 cm ).09 cm (one extra digit carried). cm Copyright 0 Nelson Education Ltd. Chapter 9: Waves and Light 9.3-5

6 Second method: dsinθn n d sinθn (6.0 cm)sin cm (one extra digit carried).0 cm Third method: The distance beteen five consecutive crests corresponds to four hole avelengths: 4 4. cm 4. cm 4.05 cm (one extra digit carried).0 cm Each of the three methods of analysis resulted in a avelength beteen.0 cm and. cm, ith an average of.0 cm. Statement: The avelength is.0 cm. (b) Ansers may vary. Sample anser: The three methods are based on data ith to significant digits. The three results differed only by one unit in the last digit. I think that these results are consistent and that no particular measurement stands out as being incorrect. Copyright 0 Nelson Education Ltd. Chapter 9: Waves and Light 9.3-6

23 Single-Slit Diffraction

$23 Single-Slit Diffraction$ 23 Single-Slit Diffraction Single-slit diffraction is another interference phenomenon. If, instead of creating a mask ith to slits, e create a mask ith one slit, and then illuminate it, e find, under certain