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Two sound speakers are driven in phase by an audio amplifier a

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Two sound speakers are driven in phase by an audio amplifier at frequency $600 Hz$ . The speed of sound is $340 m / s$ . The speakers are on the $y$ -axis, one at $y = + 1.0 m$ and the other at $y = - 1.0 m$ . A listener begins at $y = 0$ and walks along a line parallel to the $y$ -axis at a very large distance $x$ away. At $\frac{θ}{2}^{o}$ angle she will first hear a maximum (after $0^{\circ}$ ) sound intensity. Find $θ$ :

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Two sound speakers are driven in phase by an audio amplifier at frequency

600 Hz

. The speed of sound is

340 m / s

. The speakers are on the

y

-axis, one at

y = + 1.0 m

and the other at

y = - 1.0 m

. A listener begins at

y = 0

and walks along a line parallel to the

y

-axis at a very large distance

x

away. At

\frac{θ}{2}^{o}

angle she will first hear a maximum (after

0^{\circ}

) sound intensity. Find

θ

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Text solutionVerified

Path difference between sound from the two sources at a point of the line along which the listener travels =

\frac{y d}{x}

(where y is the y-coordinate of the point, d is the separation between the two sources).

Hence to obtain a maxima,

\frac{y d}{x} = λ = \frac{c}{f}

⟹ tan θ = \frac{y}{x} = \frac{c}{fd}

tan θ = \frac{340}{600 \times 2}

Using approximation,

tan θ \approx θ

⟹ θ \approx 16. 5^{\circ}

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Question Text	Two sound speakers are driven in phase by an audio amplifier at frequency $600 Hz$ . The speed of sound is $340 m / s$ . The speakers are on the $y$ -axis, one at $y = + 1.0 m$ and the other at $y = - 1.0 m$ . A listener begins at $y = 0$ and walks along a line parallel to the $y$ -axis at a very large distance $x$ away. At $\frac{θ}{2}^{o}$ angle she will first hear a maximum (after $0^{\circ}$ ) sound intensity. Find $θ$ :
Answer Type	Text solution:1
Upvotes	150