19. 0/2 points | Previous Answers SerPSE9 18.AE.001 Example 18.1 Two Speakers Dr

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19. 0/2 points | Previous Answers SerPSE9 18.AE.001 Example 18.1 Two Speakers Driven by the Same Source Two identical loudspeakers placed d1 3.89 m apart are driven by the same oscillator (see figure). A listener is originally at point O, located d2 8.00 m from the center of the line connecting the two speakers. The listener then moves to point P, which is a perpendicular distance d3 0.331 m from O, and she experiences the first minimum in sound intensity. What is the frequency of the oscillator? di SOLVE IT Conceptualize A sound wave enters a tube and is then acoustically split into two different paths before recombining at the other end. In this example, a signal representing the sound is electrically split and sent to two different loudspeakers. After leaving the speakers, the sound waves recombine at the position of the listener. Despite the difference in how the splitting occurs, the path difference discussion related to the figure can be applied here. Categorize Because the sound waves from two separate sources combine, we apply the waves in interference analysis model Analyze The figure shows the physical arrangement of the speakers, along with two shaded right triangles that can be drawn on the basis of the lengths described in the problem. The first minimum occurs when the two waves reaching the listener at point P are 180° out of phase, in other words, when their path difference r equals N2 From the shaded triangles, find the path lengths from the speakers to the listener: r1 = V (8.00 m)2 + (1.614 m)? = 8.16 m r2 = V/ (8.00 m)2 + (2.276 m)2 = 8.32 m

Explanation / Answer

for solve it:

f = 343 / 0.32 = 1097.4 Hz

MAster IT :

r1 = sqrt[ 8^2 + (3.89/2 - 0.595)^2] = 8.1131 m

r2 = sqrt[ 8^2 + (3.89/2 + 0.595)^2] = 8.3935 m

path difference = r2 - r1 = 0.280 m

and for second minimum.

path diff = 3 lambda / 2

0.280 = lambda (3/2)

lambda = 2 x 0.280 / 3 = 0.187 m  

f = v / lambda = 343 / 0.187 = 1834.6 Hz OR 1.83 kHz ......Ans

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