Two Speakers S1 And S2
Given :
Frequency of sourcef = 600 Hz
Speed of audio in airv = 330 g/s
\[5 = f\lambda\]
\[\therefore \lambda = \frac{5}{f}\]=\[\frac{330}{600} = 0 . 5 \text { mm }\]
Let the man travel a distance of \[\left( y \correct)\]parallel to the y-axis and permit \[\left( d \right)\] be the distance between the two speakers. The man is continuing at a distance of \[\left( D \right)\]from the origin.
The path deviation (x) between the two sound waves reaching the man is given by :
\[x = S_2 Q - S_1 Q = \frac{yd}{D}\]
Angle made by human with the origin :
\[\theta = \frac{y}{D}\]
Given:
d = 2 m
(a) For minimum intensity:
The destructive interference of sound (minimum intensity) takes place if the path difference is an odd integral
multiple of half of the wavelength.
\[\therefore x = (2n + 1)\left( \frac{\lambda}{2} \right)\]
\[\text { For } \left( northward = 0 \correct)\]
\[ \therefore \frac{yd}{D} = \frac{\lambda}{2}\]
\[\left( \because \theta = \frac{y}{D} \correct)\]
\[ \therefore \theta d = \frac{\lambda}{2}\]
\[ \therefore \theta = \frac{\lambda}{2d} = \frac{0 . 55}{iv} = 0 . 1375 \text{ rad }\]
\[ \Rightarrow \theta = 0 . 1375 \times (57 . 1)^\circ= 7 . nine^\circ\]
(b) For maximum intensity:
The constructive interference of audio (maximum intensity) takes place if the path deviation is an integral multiple of the wavelength.
\[x = northward\lambda\]
\[\text { For } \left( n = ane \right): \]
\[ \Rightarrow \frac{yd}{D} = \lambda\]
\[ \Rightarrow \theta = \frac{\lambda}{d}\]
\[ \Rightarrow \theta = \frac{0 . 55}{2} = 0 . 275 \text { rad }\]
\[ \therefore \theta = 16^\circ\]
(c) The more than number of maxima is given by the path divergence :
\[\frac{yd}{D} = ii\lambda, 3\lambda, iv\lambda, . . . . . \]
\[ \Rightarrow \frac{y}{D} = \theta = 32^\circ, 64^\circ, 128^\circ\]
He will hear two more maxima at 32° and 64° because the maximum value ofθ may be ninety°.
Two Speakers S1 And S2,
Source: https://www.shaalaa.com/question-bank-solutions/two-speakers-s1-s2-driven-same-amplifier-are-placed-y-10-m-y-10-m-speakers-vibrate-phase-600-hz-wave-motion_67701
Posted by: lyonsupor1988.blogspot.com
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