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A guitar string produces 3 beat/s when sounded with a 350-Hz tuning fork and 8 beat/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.
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Ch. 16 - Sound
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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TOC.tableOfContents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 16, Problema 27b
Expensive amplifier A is rated at 280 W, while the more modest amplifier B is rated at 45 W. What output wattage amp would sound about twice as loud as the 45-W amp?
Guida verificata passo dopo passo1
Understand the relationship between perceived loudness and power: The perceived loudness of a sound is proportional to the logarithm of its power. Specifically, the human ear perceives a doubling of loudness when the power increases by a factor of approximately 10^(1/10) ≈ 1.26.
Set up the equation for the power of the amplifier that would sound twice as loud as the 45-W amplifier. Let the new power be P_new. The relationship is given by: \( P_{\text{new}} = P_{\text{old}} \times 10^{1/10} \), where \( P_{\text{old}} \) is the power of the original amplifier (45 W).
Substitute \( P_{\text{old}} = 45 \ \text{W} \) into the equation: \( P_{\text{new}} = 45 \times 10^{1/10} \).
Simplify the expression: Calculate \( 10^{1/10} \), which is approximately 1.26, and multiply it by 45 to find the new power.
The result of this calculation will give the power output of the amplifier that sounds about twice as loud as the 45-W amplifier.
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Decibel Scale
The decibel (dB) scale is a logarithmic way of measuring sound intensity. An increase of about 10 dB typically corresponds to a perceived doubling of loudness. This means that to sound twice as loud, the power output must increase significantly, not linearly, due to the logarithmic nature of the scale.
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04:25
Sound Intensity Level and the Decibel Scale
Sound Power and Loudness Relationship
Sound power is the total energy emitted by a sound source per unit time, measured in watts. However, human perception of loudness does not increase linearly with power; instead, it follows a logarithmic relationship. Therefore, to achieve a perceived doubling of loudness, the power must increase by a factor of about 10 times the original power.
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04:25Sound Intensity Level and the Decibel Scale
Amplifier Ratings
Amplifier ratings indicate the maximum power output an amplifier can deliver to speakers. In this context, amplifier A at 280 W and amplifier B at 45 W suggest that A can produce significantly more sound power. Understanding these ratings helps in determining how much louder one amplifier can be compared to another, especially when considering perceived loudness.
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