Loudness of sound is directly proportional to the of ________the amplitude of vibration producing the sound.

Options

A. square
B. cube
C. inverse square
D. inverse cube

Explanation

To solve the question, we need to understand the relationship between loudness and amplitude in sound waves. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Loudness
Loudness is a measure of how loud a sound is perceived by the human ear. It is often associated with the intensity of the sound.

**Hint:** Loudness is related to how we perceive sound, and it can vary based on several factors.

### Step 2: Identify the Relationship Between Loudness and Amplitude
The loudness of sound is directly related to the amplitude of the sound wave. The greater the amplitude, the louder the sound.

**Hint:** Think about how increasing the volume on a speaker affects the sound you hear.

### Step 3: Recognize the Mathematical Relationship
The loudness of sound is not just directly proportional to the amplitude, but to the square of the amplitude. This means that if the amplitude doubles, the loudness increases by a factor of four (since 2^2 = 4).

**Hint:** Consider how squaring a number affects its value.

### Step 4: Fill in the Blank
Given the relationship, we can fill in the blank in the question. The loudness of sound is directly proportional to the square of the amplitude of vibration producing the sound.

**Final Answer:** Loudness of sound is directly proportional to the **square of** the amplitude of vibration producing the sound.

### Summary
The loudness of sound is directly proportional to the square of the amplitude of the vibrations that produce the sound.