Chapter 13. Conditions for constructive and destructive interference of waves from two sources (13-15)

Question

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{"title":"Path length difference from the two wave sources to the point where interference occurs","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"139,5,151,16\"},{\"shape\":\"rect\",\"coords\":\"119,28,128,43\"}]"} {"title":"Wavelength","description":"Wrong","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"172,2,183,16\"},{\"shape\":\"rect\",\"coords\":\"184,30,197,43\"}]"}

Question

TJnnWsyBCHsqZ81xB2cQzA==
{"title":"Path length difference from the two wave sources to the point where interference occurs","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"139,5,151,16\"},{\"shape\":\"rect\",\"coords\":\"119,28,128,43\"}]"} {"title":"Wavelength","description":"Correct!","type":"correct","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"172,2,183,16\"},{\"shape\":\"rect\",\"coords\":\"184,30,197,43\"}]"}

Review

If the path length difference \(\Delta_{\mathrm{pl}}\)is neither a whole number of wavelengths nor an odd number of half-wavelengths, the interference is neither completely constructive nor completely destructive (Figure 13-10c). Because interference of the surface waves occurs at all points in Figure 13-11, we call the overall pattern in that figure an \(\textbf{interference pattern}\).

Here’s a summary of the conditions that must be met for constructive and destructive interference:

(Note that for constructive interference, \(n = 0\) refers to the case where there is \(\textit{zero}\) path length difference, so the two waves naturally arrive in phase. This is the situation for the center yellow dot in Figure 13-11.)