Two loudspeakers emit sound waves along the x-axis. Ihe sound has maximum intensity when the speakers are 20 cm apart The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 30 cm. a What is the wavelength of the sound? b. If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?

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2022-08-16

Two loudspeakers emit sound waves along the x-axis. Ihe sound has maximum intensity when the speakers are 20 cm apart The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 30 cm. a What is the wavelength of the sound? b. If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?

Answer & Explanation

Cynthia Lester

Cynthia Lester

Beginner2022-08-17Added 22 answers

(a)The path-length difference (the extra distance traveled)
d = d f d i = 30 20 = 10 c m
The destructive interference condition is:
d = ( m + 1 2 ) λ where m=0,1,2,3...
So:
d = λ 2
λ = 2 d = 2 × 10 = 20 c m
(b)The constructive interference condition is:
d = m λ where m=0,1,2,3,...
So:
d = λ = 20 c m
Then, the new distance between the two speakers is:
d f = d i + d = 20 + 20 = 40 c m
Result:
(a)20cm (b)40cm

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