Sound intensity is inversely proportional to the square of the distance from the sound source; that is
I= k/(r)^2,
where I is the intensity, r is the distance from the sound source, and k is a constant.
Suppose that I am sitting a distance R from the TV, where its sound intnesity is I(base 1). Now you move to a seat five times as far from the TV, a distance 5R away, where the sound intensity is I(base 2).
WHAT IS THE RELATIONSHIP BETWEEN I(base 1) AND I(base 2)?
I(base 2)=_____
I have tried I(base 2)= (1/5)(I-I(base 1) BUT IT IS WRONG
PLEASE HELP:(
Intensity 1
= k / r ²
Intensity 2
= k / (5r) ²
= k / 25r ²
= (1/25) k / r ²
= (1/25) Intensity 1
Thank you sooooo much!!!!!! @plumpycat
The relationship between the sound intensities can be determined using the inverse square law. According to the given equation:
I = k / r^2
Where I is the intensity and r is the distance from the sound source.
Let's denote the initial sound intensity, when you are sitting at a distance R from the TV, as I(base 1). We can write this as:
I(base 1) = k / R^2
Now, let's denote the sound intensity when you move to a seat five times as far from the TV, a distance 5R away, as I(base 2). We can write this as:
I(base 2) = k / (5R)^2
Simplifying this equation, we get:
I(base 2) = k / 25R^2
Since both I(base 1) and I(base 2) are equal to k divided by some constant multiple of R^2, we can conclude that the relationship between I(base 1) and I(base 2) is:
I(base 2) = I(base 1) / 25
To find the relationship between I(base 1) and I(base 2), we can use the formula for sound intensity: I = k/r^2.
Let's first find the value of k using the information given. Since I(base 1) represents the sound intensity when you are at a distance R from the TV, we can write:
I(base 1) = k/(R)^2
Now, when you move to a seat five times as far from the TV, a distance 5R away, the sound intensity is given as I(base 2). So, we have:
I(base 2) = k/(5R)^2
To find the relationship between I(base 1) and I(base 2), we need to compare the two expressions. Let's rewrite the second expression by squaring the denominator:
I(base 2) = k/[25(R)^2]
Now we can compare I(base 1) and I(base 2):
I(base 2) = k/[25(R)^2] = (1/25) * (k/(R)^2) = (1/25) * I(base 1)
Therefore, the relationship between I(base 1) and I(base 2) is:
I(base 2) = (1/25) * I(base 1)
So the correct formula is I(base 2) = (1/25) * I(base 1).