Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 28 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 35 cm

Answer 1

λ = 14 cm

d = 49 cm

Step-by-step explanation:

Solution:

(a) What is the wavelength of the sound?

- The distance between two speakers is 28 cm and the intensity of the sound at any point P is maximum means there is constructive interference and the phase difference between the two waves at a point P on x axis must be an even multiple of π, and the equivalent path difference is nλ.

- Due to increase in the distance between the speakers the equivalent path difference increases and when the distance becomes 35 cm the intensity becomes zero means destructive interference and the equivalent path difference must be increase from nλ to nλ + (λ/2)

- Then the path difference can be written as:

nλ + (λ/2) - nλ = 35 - 28

(λ/2) = 7 cm

λ = 14 cm

b) If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?

- For the next maximum of intensity the path difference must be increased to (n+1)λ or the distance must be further increased by λ/2 = 14 cm. hence the intensity will be maximum again when the separation d will be:

d = 35 + 14

d = 49 cm