Interference - Frequency

1. Jun 22, 2010

SuperCass

Interference -- Frequency

1. The problem statement, all variables and given/known data

Two loudspeakers at an outdoor rock concert are located 3.5 meters apart. You are standing 16.1 meters from one of the speakers and 19 from the other. During a sound check, the technician sends the exact same frequency to both speakers while you listen. The technician starts at 20Hz and slowly increases it to 30,000Hz.
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a) What is the lowest frequency where you will hear a minimum signal ?
f = Hz
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b) What is the second lowest frequency where you will hear a minimum signal ?
f = Hz
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c) What is the lowest frequency where you will hear a maximum signal ?
f = Hz
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d) What is the second lowest frequency where you will hear a maximum signal ?
f = Hz

2. Relevant equations

$$\omega$$=2$$\pi$$f
v=$$\sqrt{T/\mu}$$

3. The attempt at a solution

I'm not sure where to start!

2. Jun 22, 2010

hikaru1221

Re: Interference -- Frequency

What is the general condition at which the net amplitude is max/min when two waves of the same frequency (and the same vibrating direction) superimpose? Hint: Something about phase difference.

3. Jun 22, 2010

SuperCass

Re: Interference -- Frequency

When there is no phase difference or the phase difference is divisible by pi?

4. Jun 22, 2010

SuperCass

Re: Interference -- Frequency

Okay so what I have done so far is found the path length difference, ($$\Delta$$L = L1 - L2).
I know that $$\Delta$$L/$$\lambda$$ = $$\Phi$$ / 2$$\Pi$$, but is this the right direction?

Where do I go from here?

5. Jun 23, 2010

hikaru1221

Re: Interference -- Frequency

The problem says nothing about the initial phase difference, so I assume that the initial signals coming out of the loudspeakers are in phase.
$$\Phi$$ is the phase difference, right? So you're on the right track ;)
1 - Now what would $$\Phi$$ be if it's maximum? And if it's minimum?
2 - Let's take the sound speed v=340m/s. You have $$\Delta L$$. So from the above equation you've just pointed out:$$f = \frac{v}{\lambda} = \frac{\Phi}{2\pi \Delta L}v$$
Subtitute $$\Phi$$ for each case (max/min), you will get f.

6. Jun 23, 2010

SuperCass

Re: Interference -- Frequency

Got it! Thank you so so much!