Textbook Question
You are trying to overhear a juicy conversation, but from your distance of 15.0 m, it sounds like only an average whisper of 20.0 dB. How close should you move to the chatterboxes for the sound level to be 60.0 dB?
Ch 16: Sound & Hearing
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 16, Problem 18a
You live on a busy street, but as a music lover, you want to reduce the traffic noise. If you install special soundreflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity (in W/m2)?
Verified step by step guidance1
Understand the relationship between sound intensity level in decibels (dB) and sound intensity in watts per square meter (W/m²). The formula to convert sound intensity level to intensity is: \( L = 10 \log_{10} \left( \frac{I}{I_0} \right) \), where \( L \) is the sound level in dB, \( I \) is the sound intensity, and \( I_0 \) is the reference intensity, typically \( 10^{-12} \text{ W/m}^2 \).
Recognize that a reduction of 30 dB means the new sound intensity level \( L' = L - 30 \). This implies that the new intensity \( I' \) is related to the original intensity \( I \) by the equation: \( L' = 10 \log_{10} \left( \frac{I'}{I_0} \right) = L - 30 \).
Use the property of logarithms to express the change in intensity: \( 10 \log_{10} \left( \frac{I'}{I_0} \right) = 10 \log_{10} \left( \frac{I}{I_0} \right) - 30 \). This simplifies to \( \log_{10} \left( \frac{I'}{I_0} \right) = \log_{10} \left( \frac{I}{I_0} \right) - 3 \).
Solve for the fraction \( \frac{I'}{I} \) by using the property of logarithms: \( \log_{10} \left( \frac{I'}{I} \right) = -3 \). This implies \( \frac{I'}{I} = 10^{-3} \).
Conclude that the sound intensity has been reduced to \( \frac{1}{1000} \) of its original value, meaning the sound intensity is now 0.1% of what it was before the installation of the sound-reflecting windows.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sound Intensity Level
Sound intensity level, measured in decibels (dB), is a logarithmic scale that quantifies the intensity of sound waves. It is calculated using the formula: L = 10 * log10(I/I0), where I is the sound intensity and I0 is the reference intensity. A change in dB represents a multiplicative change in actual sound intensity.
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Sound Intensity Level and the Decibel Scale
Decibel Scale
The decibel scale is a logarithmic scale used to measure sound intensity levels. A decrease of 10 dB corresponds to a tenfold reduction in sound intensity. Therefore, a reduction of 30 dB means the sound intensity is reduced by a factor of 1000, illustrating the non-linear nature of the scale.
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Sound Intensity
Sound intensity is the power per unit area carried by a sound wave, typically measured in watts per square meter (W/m²). It represents the energy transmitted by the wave and is directly related to the perceived loudness. Reducing sound intensity involves decreasing the energy transmitted, which can be achieved through soundproofing methods like special windows.
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Related Practice
Textbook Question
A baby's mouth is 30 cm from her father's ear and 1.50 m from her mother's ear. What is the difference between the sound intensity levels heard by the father and by the mother?
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Textbook Question
(a) By what factor must the sound intensity be increased to raise the sound intensity level by 13.0 dB? (b) Explain why you don't need to know the original sound intensity
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Textbook Question
For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0 × 10-5 Pa. Calculate the intensity.
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Textbook Question
You live on a busy street, but as a music lover, you want to reduce the traffic noise. If, instead, you reduce the intensity by half, what change (in dB) do you make in the sound intensity level?
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Textbook Question
A sound wave in air at 20°C has a frequency of 320 Hz and a displacement amplitude of 5.00 × 10-3 mm. For this sound wave calculate the pressure amplitude (in Pa)
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