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Two coherent point sound sources S_{1} and S_{2} are placed as

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Two coherent point sound sources $S_{1}$ and $S_{2}$ are placed as shown in the figure. Both are emitting sound of frequency 165 Hz. $S_{1}$ is ahead of $S_{2}$ in phase by $π -$ radian. (Speed of sound is 330 m/s) How many times maximum sound can be observed on line AB ?

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Two coherent point sound sources

S_{1}

and

S_{2}

are placed as shown in the figure. Both are emitting sound of frequency 165 Hz.

S_{1}

is ahead of

S_{2}

in phase by

π -

radian. (Speed of sound is 330 m/s) How many times maximum sound can be observed on line AB ?

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Text solutionVerified

Equation of wave

S_{1}

and

S_{2}

are

S_{1} = A s in (k x - ω t + π)

S_{2} = A s in (k x - ω t)

we know

\frac{c}{f} = λ = 2 m

interference at point A is

S_{1} - S_{2} = A s in (k x - ω t + π) - A s in (k x - ω t)

S_{1} - S_{2} = 2 A s in (\frac{k ( x _{1} + x _{2} )}{2} - ω t + \frac{π}{2}) s in (\frac{k ( x _{1} - x _{2} )}{2} + \frac{p i}{2})

k = \frac{2 π}{λ} = π

hence at point A

x_{1} = 0 x_{2} = 8 m

S_{1} - S_{2} = 2 A s in (4 π - ω t + \frac{π}{2}) s in (- 4 π + \frac{π}{2}) = 2 A cos ω t

At point A we have a maxima at

t = 0

and after every

2 m

we will get a maxima along AB hence there must 6 maximas.

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Question Text	Two coherent point sound sources $S_{1}$ and $S_{2}$ are placed as shown in the figure. Both are emitting sound of frequency 165 Hz. $S_{1}$ is ahead of $S_{2}$ in phase by $π -$ radian. (Speed of sound is 330 m/s) How many times maximum sound can be observed on line AB ?
Answer Type	Text solution:1
Upvotes	152