This is just a question about a question in Serway & Jewett's "Physics for Scientists and Engineers 3rd Ed". It's Objective Question 3 from Chapter 18, building on Example 18.1 from the text.
Two identical loudspeakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, located 8.00 m from the center of the line connecting the two speakers. The listener then moves to point P, which is a perpendicular distance 0.350 m from O, and she experiences the first minimum in sound intensity. What is the intensity at P?
a) Less than but close to the intensity at O
b) half the intensity at O
c) very low but not zero
e) indeterminate [/B]
The Attempt at a Solution
My answer to this question was d), zero. My reasoning is that a minimum occurs when the waves interfere destructively, i.e. they cancel each other out completely. This means there can be no amplitude, which means there can be no intensity.
But the solution manual says differently. It says 'The two waves must have slightly different amplitudes at P because of their different distances, so they cannot cancel each other exactly.'
I guess I'm not sure what this means or how it fits with my concept of 'minimum'. I thought the first minimum was where the path length difference that each wave travels is exactly equal to 1/2 a wavelength, so the waves are exactly 180 deg out of phase, meaning they cancel each other out perfectly.
What am I missing here? [/B]