   Chapter 14, Problem 41P

Chapter
Section
Textbook Problem

A pair of speakers separated by a distance d = 0.700 m are driven by the same oscillator at a frequency of 686 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 Figure P14.41. (a) How far must the observer walk before reaching a relative maximum in intensity? (b) How far will the observer be from the speaker when the first relative minimum is detected in the intensity? Figure P14.41

(a)

To determine
The distance the observer walks before reaching a relative maximum intensity.

Explanation

Given Info: The frequency of sound from the speaker is 686Hz.

Formula to calculate the wavelength is,

λ=vf

• v is the velocity of the sound.
• f is the frequency of sound from the horn,

The speed of sound in air is 343 m/s.

Substitute 343 m/s for v and 686 Hz for f in the above expression to get λ .

λ=343m/s686Hz=0.500m

Maximum interference occurs when the path difference is an integral multiple of wave length.

The condition for the first relative maximum is,

r=x+λ

Formula for relative maximum

r2=x2+λ2

Rearrange the expression in term of x

(b)

To determine
The distance the observer be from the speaker when the first relative minimum is detected in the intensity.

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