Understanding Inverse Proportionality in Sound Loudness

The video tutorial explains how the loudness of sound, measured in decibels, is inversely proportional to the square of the distance from the sound source. It demonstrates how to derive the inverse variation equation and calculate the variation constant using given values. The tutorial then applies this equation to determine the loudness of a leaf blower at a different distance, providing a step-by-step solution.

What is the relationship between loudness and distance in this problem?

• Directly proportional to the square of the distance

• Inversely proportional to the distance

• Inversely proportional to the square of the distance

• Directly proportional to the distance

What does the basic inverse variation equation look like?

• Y = K * X

• Y = K / X

• Y = X / K

• Y = X * K

In the context of this problem, what does the variable 'K' represent?

• The distance from the sound source

• The loudness of the sound

• The variation constant

• The square of the distance

How do you calculate the variation constant 'K' using the given values?

• Multiply loudness by distance squared

• Divide distance by loudness

• Divide loudness by distance squared

• Multiply loudness by distance

What is the value of the variation constant 'K' in this problem?

• 22,500

• 225

• 100

• 15

What mathematical operation is used to solve for 'K' in the equation 100 = K / 225?

• Division

• Addition

• Subtraction

• Multiplication

What equation is used to find the loudness at a new distance?

• L = K / D

• L = K * D

• L = D^2 / K

• L = K / D^2

If the distance is 45 feet, what is the value of D squared?

• 45

• 100

• 225

• 2025

What is the loudness of the leaf blower at 45 feet, rounded to the nearest tenth?

• 11.1 decibels

• 22.5 decibels

• 100 decibels

• 45 decibels

Why is it important to understand the concept of inverse proportionality in this problem?

• To calculate the speed of sound

• To determine the loudness at different distances

• To measure the temperature of the environment

• To find the frequency of the sound