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 18b
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?
Verified step by step guidance1
Understand the relationship between sound intensity and sound intensity level. The sound intensity level in decibels (dB) is calculated using the formula: , where is the intensity of the sound and is the reference intensity, typically W/m².
To find the change in sound intensity level when the intensity is reduced by half, consider the initial intensity and the new intensity .
Calculate the initial sound intensity level using the formula: .
Calculate the new sound intensity level with the reduced intensity: .
Determine the change in sound intensity level by subtracting the new level from the initial level: . Simplify the expression to find the change in decibels.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sound Intensity
Sound intensity refers to the power per unit area carried by a sound wave, typically measured in watts per square meter (W/m²). It quantifies the energy transmitted by the wave and is crucial for understanding how loud a sound is perceived. Reducing sound intensity can significantly decrease the perceived loudness of noise.
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Sound Intensity Level and the Decibel Scale
Decibel Scale
The decibel (dB) scale is a logarithmic unit used to measure sound intensity levels. It allows for a more manageable representation of the vast range of sound intensities humans can hear. A change in intensity by a factor of ten corresponds to a 10 dB change, making it essential for calculating changes in perceived loudness when intensity is altered.
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04:25Sound Intensity Level and the Decibel Scale
Logarithmic Relationship
The relationship between sound intensity and decibel level is logarithmic, meaning that a doubling or halving of intensity results in a specific change in dB. Specifically, halving the intensity results in a decrease of approximately 3 dB in the sound intensity level. Understanding this relationship is key to calculating changes in dB when sound intensity is modified.
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Related Practice
Textbook Question
Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if (a) the pipe is open at both ends
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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 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)?
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
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
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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