2. A speaker hanging on a wire in the exact center of a...

2. A speaker hanging on a wire in the exact center of a stadium, 25 m above the ground, and 125 m from the bleachers, produces a 702 Hz tone with 1.07 W acoustic power. a. What is the dB level directly under the speaker? b. Estimate the dB level at the bleachers

Transcript

00:01 Our question says, at a rock concert, a decibel meter registers 130 decibels when placed 2 .2 meters in front of a loudspeaker on the stage.

00:10 A, what was the power output of the speaker, assuming uniformed spherical spreading of the sound and neglecting absorption in the air? b, how far away would the sound level be a somewhat reasonable 35 decibels? okay.

00:23 Well, i wrote out what we were given.

00:24 We were given that the best decibels, which i have here is beta, 130.

00:28 And the distance is 2 .2 meters.

00:32 I wrote that as r.

00:34 Okay, so we're going to use the definition of decibels, which says that beta is equal to 10 times the log.

00:44 This is log base 10 of the intensity, which the intensity we can use to find the power divided by i0.

00:52 All right, where i not is just a constant.

00:56 Okay, so we know i not.

00:57 It's just a constant.

00:58 We know beta.

00:59 So we can find i from here.

01:01 So if we divide each side by 10, we'll have beta over 10 is equal to log i over i0, and then we raise each side to the 10th power to get rid of the log because it's log -based 10.

01:12 So that's going to give us i over i0 is equal to 10 to the beta over 10.

01:30 Then solving for i, we have i is equal to i0 beta over 10.

01:47 Well, i not is equal to, so if we plug in the values that we have, we find that i is equal to i not, which is 1 .0, which is 1 .0 times 10 to the minus 12 watts per meter squared.

02:08 It's 12.

02:13 Okay.

02:14 Multiplied by, oh, i'm sorry, i forgot up here to write a 10.

02:17 So this is supposed to be 10 to the beta over 10, not i not to the beta over 10.

02:21 So let's fix that just for clarity here.

02:23 Let's put the 10 here and then put the i -not on the other side just to make this simpler.

02:31 So this is 10 to the beta over 10 times i -0...

Question

2. A speaker hanging on a wire in the exact center of a stadium, 25 m above the ground, and 125 m from the bleachers, produces a 702 Hz tone with 1.07 W acoustic power. a. What is the dB level directly under the speaker? b. Estimate the dB level at the bleachers

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