Mathew is attending a very loud concert by the discarded. To avoid permanent ear damage he decides to move farther from the stage. Sound intensity is given by the formula I=k/d*d where k is the constant and d is the distance in metres from the listener to the source of the sound. Determine an expression for the decrease in sound intensity if mathew moves x metres farther from the stage
I= k/ d^2
Decreasing distance: I= k/(d-x)^2
now, subtract the two:
k/d^2 - k/(d-x)^2
expand (d-x)^2 to (d-x)(d-x)
now you have k/d^2 - k/(d-x)(d-x)
find common denominators...
once you do that, you will have
k(d-x)^2 / d^2 (d-x)^2 - kd^2 / d^2(d-x)(d-x)
solve it out and you will get 2kdx+kx^2 / d^2(d-x)^2
Mistake: Use (d+x)^2 instead of (d-x)^2
Well, Mathew is making a smart move by taking a step back and avoiding permanent ear damage. Let's calculate the decrease in sound intensity when Mathew moves x meters farther from the stage.
The initial sound intensity is given by I = k / d^2, where d is the initial distance from Mathew to the stage.
When Mathew moves x meters farther from the stage, the new distance becomes (d + x). So the new sound intensity can be expressed as I' = k / (d + x)^2.
To find the decrease in sound intensity, we can subtract the second equation from the first:
Decrease in sound intensity = I - I'
= (k / d^2) - (k / (d + x)^2)
And there you have it! The expression for the decrease in sound intensity when Mathew moves x meters farther from the stage is (k / d^2) - (k / (d + x)^2). Just make sure Mathew doesn't move too far, or he might not be able to hear the music at all, and that would be quite the concert tragedy!
To determine the decrease in sound intensity if Matthew moves x meters farther from the stage, we need to find the difference in sound intensities at two different distances. Let's assume Matthew's initial distance from the stage is d1, and his new distance after moving x meters is d2.
The sound intensity at the initial distance, I1, is given by the formula:
I1 = k / d1^2
The sound intensity at the new distance, I2, is given by the formula:
I2 = k / d2^2
To find the decrease in sound intensity, we subtract I2 from I1:
Decrease = I1 - I2
Substituting the values of I1 and I2, we get:
Decrease = ( k / d1^2 ) - ( k / d2^2 )
Since Matthew moved x meters farther from the stage, his new distance is d1 + x. Substituting this into the equation, we have:
Decrease = ( k / (d1 + x)^2 ) - ( k / d2^2 )
Therefore, the expression for the decrease in sound intensity if Matthew moves x meters farther from the stage is:
Decrease = ( k / (d1 + x)^2 ) - ( k / d2^2 )
Your formula makes no sense, because I could just cancel the d's and get
l = k
check your typing.
Is there a square root somewhere
I suspect something like:
" intensity is proportional to the square of the distance"