Multiple Choice
A source emits a sound in the shape of a cone, as shown in the figure below. If you measure the intensity to be 100 W/m2 at a distance of 0.5 m, what is the power of the source?
18. Waves & Sound
Sound Intensity
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A sound wave from a police siren has an intensity of 0.01 W/m2 at a certain distance. A second sound wave from an ambulance has a sound intensity level 8 dB greater than the police siren, when measured at the same distance. What is the sound intensity level (in dB) of the sound wave due to the ambulance?
A
8.01 dB
B
108 dB
C
0.063 dB
Verified step by step guidance1
Understand that sound intensity level in decibels (dB) is calculated using the formula: \( L = 10 \log_{10} \left( \frac{I}{I_0} \right) \), where \( L \) is the sound intensity level in dB, \( I \) is the intensity in W/m², and \( I_0 \) is the reference intensity, typically \( 1 \times 10^{-12} \) W/m².
Calculate the sound intensity level of the police siren using its given intensity of 0.01 W/m². Substitute \( I = 0.01 \) W/m² into the formula: \( L_{police} = 10 \log_{10} \left( \frac{0.01}{1 \times 10^{-12}} \right) \).
Recognize that the sound intensity level of the ambulance is 8 dB greater than that of the police siren. Therefore, \( L_{ambulance} = L_{police} + 8 \).
Substitute the calculated \( L_{police} \) into the equation for \( L_{ambulance} \) to find the sound intensity level of the ambulance: \( L_{ambulance} = L_{police} + 8 \).
Conclude by understanding that the sound intensity level of the ambulance is the result of adding 8 dB to the calculated sound intensity level of the police siren.
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