Two Speakers - Sound Maximum and Sound Minimum Problem


by davichi
Tags: maximum, minimum, sound, speakers
davichi
davichi is offline
#1
Jan30-10, 05:40 PM
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[tex]\lambda[/tex]

Sound Minimum:
L1' - L2 = (n+[tex]\frac{1}{2}[/tex])[tex]\lambda[/tex]

Frequency:
f = [tex]\frac{v}{\lambda}[/tex]

3. The attempt at a solution



Sound Maximum:
L1 - L2 = n[tex]\lambda[/tex]

L2 = 13.0 m
L1 = [tex]\sqrt{13.0^{2}+2.50^{2}}[/tex] = 13.23820229

L[tex]_{1}[/tex] - L[tex]_{2}[/tex] = n[tex]\lambda[/tex]
13.23820229 - 13 = n[tex]\lambda[/tex]
n[tex]\lambda[/tex] = 0.23820229

Sound Minimum
L1' - L2 =(n + [tex]\frac{1}{2}[/tex])[tex]\lambda[/tex]

L2 = 13.0 m
L1' = [tex]\sqrt{13.0^{2}+5.0^{2}}[/tex] = 13.92838828

Sub in n[tex]\lambda[/tex]= 0.23820229:

L1' - L2 = (n + [tex]\frac{1}{2}[/tex])[tex]\lambda[/tex]
13.92838828 - 13 = n[tex]\lambda[/tex] + [tex]\lambda[/tex]/2
[tex]\lambda[/tex]/2 = 0.92838828 - 0.23820229
[tex]\lambda[/tex] = 1.380371974

Sub in [tex]\lambda[/tex] = 1.380371974:
f = [tex]\frac{v}{\lambda}[/tex]
f = [tex]\frac{340}{1.380371974}[/tex]
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.
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
rl.bhat
rl.bhat is offline
#2
Jan31-10, 07:51 AM
HW Helper
P: 4,442
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
davichi is offline
#3
Jan31-10, 08:57 AM
P: 2
Ooh.. no wonder. Thank you very much!


Register to reply

Related Discussions
Directional (ultra)sound speakers General Physics 5
Hooking up surround sound, how to disable tv's speakers? Computing & Technology 6
Sound: Speakers Woofers vs. Tweeters Advanced Physics Homework 2
Speakers & sound waves Introductory Physics Homework 6
Speakers sound level at a certain point. Introductory Physics Homework 1