Problem

Two loudspeakers are placed at either end of a gy…

01:43

Problem 58 Hard Difficulty

Predict/Calculate Two violinists, one directly behind the other,
play for a listener directly in front of them. Both violinists sound
concert $\mathrm{A}(440 \mathrm{Hz})$ . (a) What is the smallest separation between
the violinists that will produce destructive interference for the listener? (b) Does this smallest separation increase or decrease if the
violinists produce a note with a higher frequency? (c) Repeat part
(a) for violinists who produce sounds of 540 $\mathrm{Hz}$ .

Answer

a) 0.390 $\mathrm{m}$
b) shorter minimum separation
c) 0.318 $\mathrm{m}$

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Physics 101 Mechanics

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Video Transcript

in Problem 58. We have to violinist sitting one behind the other and then directly in front of them is a listener. And the question I ask, What's the smallest separation between the two violinist to have destroy active interference for the listener when they play a note that has a frequency of 4 40? Well, we know the conditions for destructive interference. There's destructive interference when the path length difference is half a wavelength or, um, the rehabs of wavelength or 5/2 civil wavelength or 7/2 salute wavelength. You got it. Um, so there their separation for the smallest separation would be when they have a pathway difference of careful wavelength. So we just have to find what, half a wave like this. So I know that the wavelength for sound I'm gonna follow the wave equation. The velocity of sound is 3 43 I'm looking for the wavelength. When the frequency is for 40 I just divide and I get that has a wavelength of 0.780 so half a wavelength will be half of 0.780 And that is point 390 so that's how four report. There's violinist must be sitting the next question. Ask with that separation increase or decrease tohave destructive interference when the frequency is increased. Well, if I think of my equation, if my frequency is increasing, my wavelength must be decreasing because the speed of sound doesn't change. So if my wavelength is decreasing, then my separation must decrease because my separation is half of the wavelength. And then part See, I'm asked to find what their separation would be when they play a note of 5 40 hurts some funding the wavelength when the frequency is 5 40 speed of sound. 3 43 I'm looking for the wavelength. When the frequency is 5 40 I divide both sides by 5 40 and I get a wave like this. 0.635 So half a wavelength it's half of 0.635 point 318 meters. It decreases just like we said it would

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