Two Speakers - Sound Maximum and Sound Minimum Problem

[davichi]

[Solved] Two Speakers - Sound Maximum and Sound Minimum Problem

Hi, I am having difficulty solving the following problem:

Homework Statement

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.

Homework Equations

Sound Maximum:
L1 - L2 = n$$\lambda$$

Sound Minimum:
L1' - L2 = (n+$$\frac{1}{2}$$)$$\lambda$$

Frequency:
f = $$\frac{v}{\lambda}$$

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.

 

[rl.bhat]

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.

 

[davichi]

Ooh.. no wonder. Thank you very much!