Domanda del libro di testo
A 572-Hz longitudinal wave in air has a speed of 345 m/s. How much time is required for the phase to change by 90° at a given point in space?
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Ch. 15 - Wave Motion
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 15, Problema 28
A transverse wave with a frequency of 220 Hz and a wavelength of 10.0 cm is traveling along a cord. The maximum speed of particles on the cord is 0.10 the wave speed. What is the amplitude of the wave?
Guida verificata passo dopo passo1
Step 1: Start by identifying the given values in the problem. The frequency \( f \) is 220 Hz, the wavelength \( \lambda \) is 10.0 cm (convert to meters: \( \lambda = 0.10 \ \text{m} \)), and the maximum particle speed \( v_{\text{particle, max}} \) is 0.10 times the wave speed \( v_{\text{wave}} \).
Step 2: Use the wave speed formula \( v_{\text{wave}} = f \cdot \lambda \) to calculate the wave speed. Substitute the given values of \( f \) and \( \lambda \) into the formula to find \( v_{\text{wave}} \).
Step 3: Recall the relationship between the maximum particle speed \( v_{\text{particle, max}} \), the wave amplitude \( A \), the angular frequency \( \omega \), and the wave speed. The formula is \( v_{\text{particle, max}} = A \cdot \omega \), where \( \omega = 2 \pi f \).
Step 4: Substitute \( \omega = 2 \pi f \) into the formula for \( v_{\text{particle, max}} \), giving \( v_{\text{particle, max}} = A \cdot 2 \pi f \). Rearrange this equation to solve for the amplitude \( A \): \( A = \frac{v_{\text{particle, max}}}{2 \pi f} \).
Step 5: Substitute the known values of \( v_{\text{particle, max}} = 0.10 \cdot v_{\text{wave}} \), \( f = 220 \ \text{Hz} \), and \( v_{\text{wave}} \) (calculated in Step 2) into the formula for \( A \). Simplify to find the amplitude of the wave.
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Wave Speed
Wave speed is the speed at which a wave propagates through a medium. It can be calculated using the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. In this case, with a frequency of 220 Hz and a wavelength of 10.0 cm, the wave speed can be determined, which is essential for understanding the motion of the wave.
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Percorso guidato
07:19
Intro to Waves and Wave Speed
Amplitude
Amplitude is the maximum displacement of particles from their equilibrium position in a wave. It represents the height of the wave and is directly related to the energy carried by the wave. In this problem, the amplitude can be found using the relationship between the maximum speed of the particles and the wave speed, as the maximum speed is a fraction of the wave speed.
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Percorso guidato
04:24Amplitude Decay in an LRC Circuit
Transverse Waves
Transverse waves are waves in which the particle displacement is perpendicular to the direction of wave propagation. In the context of a cord, as the wave travels along the cord, the particles move up and down while the wave itself moves horizontally. Understanding the nature of transverse waves is crucial for analyzing the motion of particles and the characteristics of the wave.
Video consigliato:
Percorso guidato
07:32Transverse Velocity of Waves
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