A pair of speakers separated by distance d = 0.900 m are driven by the same oscillator at a frequency of 670 Hz. An observer originally positioned at one of the speakers begins to walk along a line perpendicular to the line joining the speakers as in the figure below.

Question

(a) How far must the observer walk before reaching a relative maximum in intensity?

Here I calculated the wavelength 343/670= 0.511940

Then I did (0.9)^2 - (0.5119)^2/(2*0.5119) and got 0.535m as my answer, which is correct.

(b) How far will the observer be from the speaker when the first relative minimum is detected in the intensity?

I can't seem to find the right answer for part b.

I did [(0.9)^2-((0.5119)^2/4)]/0.5119
to get 1.45

but that is not the correct answer. Can someone tell me what I did wrong? thank you!

Answer 1

On B, it is a right triangle
you want the distances to be half wavelength apart, or .512/2 meters different.

d= distance walked
x= distance from far speaker
x-d=1/2 wavelength. or x=.512/2 + d
Now the right traiangle:
.9^2+d^2=x^2 or
.9^2+d^2=(.256+d)^2
.9^2+d^2=.256^2+d^2+512d
(.81-.256^2 )/.512 = d

which agrees with your answer.

Answer 2

how did you get this value for part a? I tried your numbers and it gave me 0.554