Two identical loudspeakers are driven in phase by a common oscillator at 810 Hz

Question

Two identical loudspeakers are driven in phase by a common oscillator at 810 Hz and face each other at a distance of 1.20 m. Locate the points along the line joining the two speakers where relative minima of sound pressure amplitude would be expected. (Take the speed of sound in air to be 343 m/s. Choose one speaker as the origin and give your answers in order of increasing distance from this speaker. Enter 'none' in all unused answer boxes.) Distance from Minima speaker (m) 494135 X st If the speakers are driven in phase, will an antinode or a node occur at the midontbetween the speakers? 2nd 3rd 4 1' 6th 4th 28240 00679X 70586 91759 1.129 What is the relationship between the wavelength and the distance between nodes? none

Explanation / Answer

In order to find the solution, first we need to find wavelength of sound, i.e.

= v/f = 343/810 = 0.423 m

We will also need /2 and /4

/2 = 0.2117 m        /4 = 0.1058 m

If we stand midway between the two speakers that are driven in phase, then the travel length of the sound at the midway points will be equal. That means right in the center you will have constructive interference.

If the distance "2d" is half a wavelength, that is a condition for destructive interference So

if 2d = /2, we have our first minima. That will be wher d = /4, which is 0.1058 m from the center.

If the center is 0.6 m, and you move 0.1058 m toward either speaker, you will have a minima.

Starting at 0.6 m (the middle), the first minima away from that wil be

0.6 + /4    and 0.6 - /4

0.6 + 0.1058 = 0.7058 m 0.6 - 0.1058 = 0.4942 m

Next, continue adding (to the right) or subtracting (to the left) /2 from the successive points..

0.7058 + 0.2117 = 0.9175 m

0.9175 + 0.2117 = 1.129 m

In the other direction,

0.4942 - 0.2117 = 0.2825 m

0.2825 - 0.2117 = 0.0708 m

So, the order of distances from the smallest distance to the largest distance is given by,

1) 0.0708 m

2) 0.2825m

3) 0.4942 m

4) 0.7058 m

5) 0.9175 m

6) 1.129 m

7) None

(Please rate my answer if you find it helpful, good luck...)

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