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 17a
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)
Verified step by step guidance1
First, understand that the pressure amplitude of a sound wave is related to its displacement amplitude, frequency, and the properties of the medium (air in this case). The formula to calculate the pressure amplitude (ΔP) is: ΔP = ρ * v * ω * s₀, where ρ is the density of air, v is the speed of sound in air, ω is the angular frequency, and s₀ is the displacement amplitude.
Determine the density of air (ρ) at 20°C, which is approximately 1.204 kg/m³.
Calculate the speed of sound (v) in air at 20°C. The speed of sound in air can be approximated by the formula: v = 331.4 + 0.6 * T, where T is the temperature in Celsius. Substitute T = 20°C to find v.
Find the angular frequency (ω) using the formula: ω = 2 * π * f, where f is the frequency of the sound wave. Substitute f = 320 Hz to calculate ω.
Convert the displacement amplitude (s₀) from millimeters to meters by multiplying 5.00 * 10^-3 mm by 10^-3. Now, substitute all known values into the pressure amplitude formula: ΔP = ρ * v * ω * s₀, and solve for ΔP.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sound Wave Properties
Sound waves are longitudinal waves characterized by frequency, wavelength, amplitude, and speed. Frequency, measured in Hertz (Hz), indicates how many cycles occur per second. Amplitude refers to the maximum displacement of particles in the medium, affecting the wave's intensity and loudness.
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Standing Sound Waves
Pressure Amplitude
Pressure amplitude in a sound wave is the maximum change in pressure from the ambient atmospheric pressure caused by the wave. It is related to the displacement amplitude and frequency of the wave, and can be calculated using the formula involving the medium's density and speed of sound.
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Speed of Sound in Air
The speed of sound in air is influenced by temperature, with a typical value of approximately 343 meters per second at 20°C. This speed is crucial for calculating wave properties like wavelength and pressure amplitude, as it determines how quickly sound waves propagate through the medium.
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Related Practice
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
Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate. Typically, the diameter of this membrane is about 8.4 mm in humans. How much energy is delivered to the eardrum each second when someone whispers (20 dB) a secret in your ear?
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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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