Produces a sound level of 53 db a single student speaking...

produces a sound level of 53 dB. A single student speaking normally produces a sound level of 40 dB. How many students are in the room? Assume each student in the group speaks at the same sound level as did the single student.

Transcript

00:01 In this problem, a group of students in a classroom produce a sound level of 53 decibel.

00:07 A single student speaking normally produces a sound level of 40 decibel.

00:20 How many students are there in the room? it is asked to assume each student in the group speaks at the same level as in the of the single.

00:37 Person all right so now what do we know okay so for a single student it is said that sound level is produced of 40 decibel right this is for a single student right so let us see let us call it as case one all right so now we are also assuming let us say 53 decibel is produced by x students this is what we have to find out this is what we have to find out right so this is case two all right so now what is the formula for intensity and sound level so this is the relationship between intensity and sound level all right so which is represented as beta beta as in decibel right this is nothing but this is a sound level all right so now this is given by beta equals to 10 log i by i not right so 10 db is in decibels right okay so now moving forward for the case one for one student if we put the values in equation number one for a single student we will get beta 1 equals to let us say this is beta 1 so this is equal to 40 decibels equals to 10 log i by i not right so this is this is intensity for you can say this is intensity for these students right this is for one student right so this is the fundamental intensity that is i not right so now let us say this is equation number two right so this is for single student now for x number of students can we say that the intensity will be x times right of i that is a one person let us say for a one person the intensity was i right so we can write this formula is like that beta 2 equals to 53 decibels equals to 10 log x i by i not right so this is equation number 3 all right okay so now uh in this way we can say that beta 2 minus beta 1 let us say subtract equation 2 by 3 right so by equation 3, right? so this will give us beta 2 minus beta 1 equals to 53 minus 40 equals to 10 log x, right? so this is never forget that this log isn't base 10.

03:35 So now this will give us 113 equals to 10 log x, which is nothing but x equals to 10 to the power when it goes like this, 1 .3, right? 13 .10 is 1 .3 and it has as it has log base 10 that means this will convert it into 10 to the power minus 10 to the power 1 .3 all right so this will be giving us approximately equals to approximately equals to 19 .95 right so this is not given in option or if it is not given in option then you can assume it as 20 is 2 .10...

Question

produces a sound level of 53 dB. A single student speaking normally produces a sound level of 40 dB. How many students are in the room? Assume each student in the group speaks at the same sound level as did the single student.

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