AP Physics 1 Questions on Sound Intensity with Solutions

📚 Quick Study Guide

• 👂 Sound Intensity (I): Measures the power of a sound wave per unit area. Units are Watts per square meter ($W/m^2$).
• 📏 Area: For a point source, sound waves spread spherically. Area $A = 4\pi r^2$, where $r$ is the distance from the source.
• 🔊 Formula for Intensity: $I = \frac{P}{A}$, where $P$ is the power of the sound source and $A$ is the area over which the sound is distributed.
• 📉 Inverse Square Law: Intensity decreases with the square of the distance from the source: $I \propto \frac{1}{r^2}$.
• 📢 Sound Level ($\beta$): Measured in decibels (dB). $\beta = 10 \log_{10}(\frac{I}{I_0})$, where $I_0 = 10^{-12} W/m^2$ is the threshold of hearing.
• ➕ Intensity Change: If the sound intensity increases by a factor of 10, the sound level increases by 10 dB.
• 🎛️ Power: The rate at which energy is transferred by the sound wave. Measured in Watts (W).

Practice Quiz

1. A sound source emits power $P$ uniformly in all directions. At a distance $r$ from the source, the intensity is $I$. What is the intensity at a distance $2r$ from the source?

   1. A) $4I$
   2. B) $2I$
   3. C) $I/2$
   4. D) $I/4$

2. The sound level at a certain distance from a source is 60 dB. If the intensity is increased by a factor of 100, what is the new sound level?

   1. A) 62 dB
   2. B) 80 dB
   3. C) 120 dB
   4. D) 6000 dB

3. Two identical sound sources emit sound with an intensity of $I$ each. If both sources are turned on simultaneously at the same location, what is the resulting intensity?

   1. A) $I$
   2. B) $2I$
   3. C) $4I$
   4. D) $\sqrt{2}I$

4. The intensity of a sound wave is $10^{-6} W/m^2$. What is the corresponding sound level in decibels?

   1. A) 6 dB
   2. B) 30 dB
   3. C) 60 dB
   4. D) 100 dB

5. If the distance from a sound source is doubled, by what factor does the intensity change?

   1. A) 1/4
   2. B) 1/2
   3. C) 2
   4. D) 4

6. A machine produces a sound level of 80 dB. How much more intense is this sound compared to the threshold of hearing ($I_0 = 10^{-12} W/m^2$) ?

   1. A) $10^{-20}$ times
   2. B) $10^{-8}$ times
   3. C) $10^{8}$ times
   4. D) $10^{20}$ times

7. A point source emits sound waves with a power of 100 W. What is the intensity at a distance of 5 meters from the source?

   1. A) $0.32 W/m^2$
   2. B) $1.0 W/m^2$
   3. C) $3.2 W/m^2$
   4. D) $12.56 W/m^2$