# Two Speakers - Sound Maximum and Sound Minimum Problem

by davichi
Tags: maximum, minimum, sound, speakers
 P: 2 Hi, I am having difficulty solving the following problem: 1. The problem statement, all variables and given/known data Two loudspeakers 5.0 m apart are playing the same frequency. If you stand 13.0 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 13.0 m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers. What is the frequency of the sound? Assume a sound speed of 340 m/s. 2. Relevant equations Sound Maximum: L1 - L2 = n$$\lambda$$ Sound Minimum: L1' - L2 = (n+$$\frac{1}{2}$$)$$\lambda$$ Frequency: f = $$\frac{v}{\lambda}$$ 3. The attempt at a solution Sound Maximum: L1 - L2 = n$$\lambda$$ L2 = 13.0 m L1 = $$\sqrt{13.0^{2}+2.50^{2}}$$ = 13.23820229 L$$_{1}$$ - L$$_{2}$$ = n$$\lambda$$ 13.23820229 - 13 = n$$\lambda$$ n$$\lambda$$ = 0.23820229 Sound Minimum L1' - L2 =(n + $$\frac{1}{2}$$)$$\lambda$$ L2 = 13.0 m L1' = $$\sqrt{13.0^{2}+5.0^{2}}$$ = 13.92838828 Sub in n$$\lambda$$= 0.23820229: L1' - L2 = (n + $$\frac{1}{2}$$)$$\lambda$$ 13.92838828 - 13 = n$$\lambda$$ + $$\lambda$$/2 $$\lambda$$/2 = 0.92838828 - 0.23820229 $$\lambda$$ = 1.380371974 Sub in $$\lambda$$ = 1.380371974: f = $$\frac{v}{\lambda}$$ f = $$\frac{340}{1.380371974}$$ f = 246.3104195 Hz I'm not sure if my approach is wrong or if I'm interpreting the question incorrectly. Any help would be greatly appreciated! Thanks.
 HW Helper P: 4,433 In the central position the two speakers are at equal distance. So the path difference is zero. In between the first and the second position, there is neither a maximum nor a minimum. So at the second position ( l1' - l2) = λ/2.
 P: 2 Ooh.. no wonder. Thank you very much!

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