Question

A pair of speakers separated by .700 m are driven by the sameoscillator at a frequency of 690 Hz. An observer originallypositioned at one of the speak

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asked 2021-05-09
A pair of speakers separated by .700 m are driven by the sameoscillator at a frequency of 690 Hz. An observer originallypositioned at one of the speakers begins to walk along a lineperpendicular to the line joining the speakers.
a. How far must the observer walk before reaching a relativemaximum in intensity?
b. How far will the observer be from the speaker when the firstrelative minimum is detected in the intensity?

Answers (1)

2021-05-11
image
Given:
the wavelength of the sound will be
\(\displaystyle\lambda={\frac{{{v}}}{{{f}}}}\)
\(\displaystyle={\frac{{{345}\frac{{m}}{{s}}}}{{{690}{H}{z}}}}\)
a) for the first relative maximum we get
\(\displaystyle{d}_{{1}}={d}_{{2}}+\lambda\)
from the figure using the pythagorous theorem we get
\(\displaystyle{\left({d}_{{2}}+\lambda\right)}^{{2}}={{d}_{{2}}^{{2}}}+{\left({0.820}{m}\right)}^{{2}}\)
\(\displaystyle{d}_{{2}}=\ldots\)
b) for the first relative minimum we get
\(\displaystyle{d}_{{1}}={d}_{{2}}+{\left(\frac{\lambda}{{2}}\right)}\)
from the figure using the pythagoroustheorem we get
\(\displaystyle{\left({d}_{{2}}+{\left(\frac{\lambda}{{2}}\right)}\right)}^{{2}}={{d}_{{2}}^{{2}}}+{\left({0.820}{m}\right)}^{{2}}\)
\(\displaystyle{d}_{{2}}=\ldots\)
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