Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 19 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 29 cm.

What is the wavelength of the sound?
Express your answer using two significant figures.
\lambda ={\rm cm}
Part B
If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?
Express your answer using two significant figures.

Explanation:

The the observer must not be stationed between speakers . Let its position be d cm from one of the speaker. When sound has maximum intensity , the the two sounds reaching his ear must have constructive interference and during zero intensity , they must have destructive interference. Distance between sources will be equal to path difference.

For constructive interference

n λ = path diff

= 19 cm

For destructive interference

(2n+1) λ /2= path diff

= 29 cm

n λ +  λ /2 = 29

19 +  λ /2 = 29

λ  = 20 cm

B )

The path difference of 19 cm corresponds to constructive interference or maximum sound intensity . Wave length is 20 cm . Therefore , next path difference that can create condition of constructive interference will be 19 + 20 = 39 cm . Present path difference is 29 cm. So the distance between the speaker must be increased to 39 cm , so that path difference becomes 39 cm and constructive interference takes place.

ANS 39 cm .

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