Textbook Question
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?
Ch. 15 - Wave Motion
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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Table of contents
- 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: 9780137488179Not the one you use?Change textbook
Chapter 15, Problem 29a
A 572-Hz longitudinal wave in air has a speed of 345 m/s. What is the wavelength?
Verified step by step guidance1
Identify the relationship between the speed of a wave, its frequency, and its wavelength. The formula is: , where is the wave speed, is the frequency, and is the wavelength.
Rearrange the formula to solve for the wavelength : .
Substitute the given values into the formula. The wave speed is 345 m/s, and the frequency is 572 Hz.
Perform the division to calculate the wavelength: . Ensure the units are consistent, with speed in meters per second and frequency in hertz.
The result of the division will give the wavelength in meters, which represents the distance between successive compressions or rarefactions in the longitudinal wave.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wave Speed
Wave speed is the distance a wave travels per unit of time. In the context of sound waves, it is determined by the medium through which the wave is traveling. For air at room temperature, the speed of sound is approximately 345 m/s, which is crucial for calculating other wave properties.
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Frequency
Frequency is the number of cycles of a wave that pass a point in one second, measured in hertz (Hz). In this question, the frequency of the longitudinal wave is given as 572 Hz, indicating that 572 cycles occur every second. Frequency is directly related to the energy of the wave and is essential for determining its wavelength.
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Wavelength
Wavelength is the distance between successive crests (or troughs) of a wave. It can be calculated using the formula: wavelength = speed / frequency. In this case, knowing the speed of the wave (345 m/s) and its frequency (572 Hz) allows us to find the wavelength, which is a fundamental property of the wave.
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Related Practice
Textbook Question
Consider the point x = 1.00 m on the cord of Example 15–6. Determine the maximum acceleration of this point.
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Textbook Question
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?
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Textbook Question
A 572-Hz longitudinal wave in air has a speed of 345 m/s. At a particular instant, what is the phase difference (in degrees) between two points 4.4 cm apart?
Textbook Question
Write the equation for the wave in Problem 29 traveling to the right, if its amplitude is 0.020 cm, and D = - 0.020 cm, at t = 0 and x = 0.
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Textbook Question
A transverse wave pulse travels to the right along a string with a speed v = 2.0 m/s. At the shape of the pulse is given by the function D = 0.45 cos (2.6x + 1.2), where D and x are in meters. Determine a formula for the wave pulse at any time t assuming there are no frictional losses.
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