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dabicvietboi
02.12.2020 •
Physics
Suppose that the separation between two speakers A and B is 6.60 m and the speakers are vibrating in-phase. They are playing identical 126-Hz tones and the speed of sound is 343 m/s. An observer is seated at a position directly facing speaker B in such a way that his line of sight extending to B is perpendicular to the imaginary line between A and B. What is the largest possible distance between speaker B and the observer, such that he observes destructive interference
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Ответ:
Complete question
The diagram for this question is shown on the first uploaded image
The largest possible distance is![e = 15.33 \ m](/tpl/images/0941/5227/e60fe.png)
Explanation:
From the question we are told that
The separation between Speaker at position A and B is AB = 6.60 m
The frequency of the tune which the speaker are playing is![f = 126 \ Hz](/tpl/images/0941/5227/58b9e.png)
The speed of sound is![v = 343 \ m/s](/tpl/images/0941/5227/64036.png)
Generally the wavelength of the tune playing is mathematically represented as
=>![\lambda = \frac{343}{ 126}](/tpl/images/0941/5227/4d6a5.png)
=>![\lambda = 2.72 \ m](/tpl/images/0941/5227/f3a10.png)
Let the observer be at position D
Generally the distance A and is mathematically evaluated using Pythagoras theorem as
Let BC = e
So
Generally the path difference between the first and the second speaker from the observer point of view is mathematically represented as
=>![P = \sqrt{6.60 ^2 + e^2} - e](/tpl/images/0941/5227/72e34.png)
Generally the condition for destructive interference is mathematically represented as
Here n is the order of the fringe which is one
=>![\sqrt{6.60 ^2 + e^2} - e = (2 * 1 - 1 )\frac{2.72}{2}](/tpl/images/0941/5227/04733.png)
=>![\sqrt{6.60 ^2 + e^2} - e = 1.36](/tpl/images/0941/5227/faabb.png)
=>![6.60 ^2 + e^2 =( 1.36 +e)^2](/tpl/images/0941/5227/87056.png)
=>![6.60 ^2 + e^2 =1.8496 + 2.72e +e^2](/tpl/images/0941/5227/66b12.png)
=>![e = 15.33 \ m](/tpl/images/0941/5227/e60fe.png)
Ответ: