Sound Intensity Level (Decibels) Quiz with Answer Key

📚 Quick Study Guide

🔍 Understanding Sound Intensity: Sound intensity (I) is the power (P) of a sound wave per unit area (A). Measured in Watts per square meter ($W/m^2$). 🔢 Formula for Sound Intensity: $I = \frac{P}{A}$ 👂 The Threshold of Hearing: The quietest sound a human can hear is $I_0 = 10^{-12} W/m^2$. 🔊 Sound Intensity Level (Decibels): The sound intensity level ($\beta$) is measured in decibels (dB) and is defined relative to the threshold of hearing. 📐 Formula for Decibels: $\beta = 10 \log_{10}(\frac{I}{I_0})$ ➕ Adding Decibels: Decibels are logarithmic, so you can't simply add them linearly. Use $I_{total} = I_1 + I_2 + ...$ and then convert back to decibels using the formula above. 💡 Tips: Remember that an increase of 10 dB corresponds to a tenfold increase in sound intensity.

🧪 Practice Quiz

1. What is the reference intensity ($I_0$) used to calculate sound intensity level in decibels?
   1. $10^{-10} W/m^2$
   2. $10^{-12} W/m^2$
   3. $1 W/m^2$
   4. $0 W/m^2$
2. If the sound intensity doubles, approximately how many decibels does the sound intensity level increase?
   1. 3 dB
   2. 6 dB
   3. 10 dB
   4. 20 dB
3. A sound has an intensity of $10^{-6} W/m^2$. What is the sound intensity level in decibels?
   1. 30 dB
   2. 60 dB
   3. 90 dB
   4. 120 dB
4. Two identical sound sources each produce a sound intensity level of 50 dB. If both sources are turned on simultaneously, what is the resulting sound intensity level?
   1. 50 dB
   2. 53 dB
   3. 100 dB
   4. 2500 dB
5. What happens to the perceived loudness of a sound when the sound intensity level increases by 10 dB?
   1. It doubles.
   2. It is halved.
   3. It increases by a factor of 10.
   4. It remains the same.
6. A machine produces a sound intensity level of 80 dB at a distance of 1 meter. Assuming the sound radiates uniformly in all directions, what would be the sound intensity level at a distance of 2 meters?
   1. 20 dB
   2. 40 dB
   3. 74 dB
   4. 80 dB
7. If the sound intensity is increased by a factor of 1000, what is the corresponding increase in the sound intensity level in decibels?
   1. 10 dB
   2. 20 dB
   3. 30 dB
   4. 100 dB