- #1

jybe

- 41

- 1

## Homework Statement

Two identical loudspeakers

are driven in phase by the same amplifier at a frequency of 680 Hz. The

speakers are 4.6 m apart. An observer stands 9 m away

from one of the speakers as shown. The observer

then starts moving directly towards the closest speaker.

How far does the observer have to move to hear

their first sound minimum? The speed of sound is 340 m/s

## Homework Equations

## The Attempt at a Solution

I found a solution:

Frequency of sound, f = 680 Hz

Velocity of sound, v = 340 m/s

Wavelength of sound,

= 340/680 = 0.5 m

Consider that after moving a distance 'd', the observer hear a minimum.

Distance to the first speaker, D1 = SQRT[(9 - d)2 + 4.62]

Distance to the second speaker, D2 = 9 - d

The condition of destructive interference is that,

D1 - D2 = n

SQRT[(9 - d)2 + 4.62] - (9 - d) = n

**There are no solutions for n = 1 and n = 3, For n = 5,**

SQRT[(9 - d)2 + 4.62] - (9 - d) = 1.25

SQRT[(9 - d)2 + 4.62] = 10.25 - d

Squaring both the sides,

[(9 - d)2 + 4.62] = [9.25 - d]2

81 + d2 - 18d + 21.16 = 105.0625 - 20.5d + d2

102.16 - 18d = 105.0625 - 20.5d

2.5d = 2.9025

d = 1.161 m

My question is about the bolded part. How was it determined that there are no solutions for n=1 and n=3? How do you know what n can equal? Thanks.