Two speakers connected to the same source of fixed frequency are place...
Sound from S1 and S2 will interfere at the point on the circumference of the circle.
At A, path difference between two sounds is 0 m.
At B, path difference between two sounds is S1B−S2B=2 m.
From A to B, along the circumference, the path difference increases. Hence maxima and minima will be observed along the circumference. At B, 5th maxima is observed.
⇒ ΔxB = 2= 5λ
⇒ λ = 0.4 m
Two speakers connected to the same source of fixed frequency are place...
Solution:
Given, distance between the speakers, d = 2.0 m
Distance between the midpoint of the speakers and the microphone, L = 4.0 m
Number of maximum responses observed during rotation, n = 5
Finding the wavelength of sound wave
Let λ be the wavelength of the sound wave.
When the speakers are in line with the microphone, the path difference between the waves reaching the microphone from the two speakers is given by λ/2.
Constructive interference occurs at the microphone when the path difference is an integer multiple of the wavelength, i.e.,
d sin θ = nλ, where n = 0, 1, 2, 3, ...
When the speakers are perpendicular to the line joining them and the microphone is at the midpoint, the path difference is zero and hence the distance between two speakers, d = λ/2.
When the speakers are in line with the microphone, the distance between the midpoint of the speakers and the microphone remains unchanged, i.e., L = 4.0 m.
Using the above equations, we get
d sin θ = nλ
2 sin θ = nλ / 2
2 sin θ = L / n
sin θ = L / (2n)
When n = 5, sin θ = 0.4
Therefore, λ = 2d sin θ = 2 × 2.0 × 0.4 = 1.6 m
Hence, the wavelength of the sound wave is 0.4 m.
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