📚 Topic Summary
Sound wave loudness is often measured in decibels (dB), which is a logarithmic unit that describes the ratio of a sound's intensity to a reference intensity. Because the human ear can detect a huge range of sound intensities, the decibel scale makes it easier to express and compare loudness. Decibel calculations involve using logarithms to relate sound intensity to perceived loudness. 🤓
The formula to calculate sound level ($L$) in decibels is:
$L = 10 \log_{10}(\frac{I}{I_0})$
where $I$ is the intensity of the sound and $I_0$ is the reference intensity (usually $10^{-12} \text{ W/m}^2$, the threshold of human hearing). Remember, a small change in decibels can mean a big change in sound intensity! 👂
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Decibel (dB) |
A. The power of a sound wave per unit area. |
| 2. Intensity (I) |
B. A unit used to express relative differences in signal strength. |
| 3. Threshold of Hearing ($I_0$) |
C. The quietest sound most humans can hear. |
| 4. Logarithm |
D. A mathematical function that is the inverse operation to exponentiation. |
| 5. Sound Pressure Level |
E. A measure of the effective pressure of a sound relative to a reference value. |
Match the letters to the numbers (e.g., 1-B, 2-A, etc.)
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct words.
The loudness of a sound is measured in __________. This scale is __________ because it uses logarithms to compress a wide range of sound __________ into a manageable range. A small change in decibels corresponds to a __________ change in sound intensity. The reference intensity, also known as the __________ of hearing, is typically $10^{-12} \text{ W/m}^2$.
Word Bank: decibels, logarithmic, intensities, significant, threshold
🤔 Part C: Critical Thinking
Explain in your own words why a logarithmic scale is useful for measuring sound intensity.