Textbook Question
Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.
<Image>
Sketch the shape of the string at the end of 6.0 s.
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Ch 15: Mechanical Waves
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 15, Problem 38b
A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the second overtone?
Verified step by step guidance1
First, understand that the second overtone in a stretched string corresponds to the third harmonic. In a string fixed at both ends, the number of antinodes corresponds to the harmonic number.
For the third harmonic, the string will have three antinodes and two nodes (excluding the endpoints). The wavelength \( \lambda \) of the third harmonic is given by \( \lambda = \frac{2L}{3} \), where \( L \) is the length of the string.
Substitute the given length of the rope \( L = 1.50 \text{ m} \) into the wavelength formula to find the wavelength of the third harmonic.
The frequency \( f \) of a wave is related to its speed \( v \) and wavelength \( \lambda \) by the equation \( f = \frac{v}{\lambda} \). Use the wave speed \( v = 62.0 \text{ m/s} \) and the wavelength calculated in the previous step to find the frequency of the third harmonic.
By following these steps, you will determine both the wavelength and frequency of the second overtone (third harmonic) on the rope.
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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 rate at which a wave propagates through a medium, calculated as the product of frequency and wavelength. In this scenario, the wave speed is given as 62.0 m/s, which is crucial for determining the wavelength and frequency of the wave on the rope.
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07:19
Intro to Waves and Wave Speed
Standing Waves and Overtones
Standing waves occur when waves reflect back and forth between fixed points, creating nodes and antinodes. Overtones are higher frequency modes of vibration. The second overtone corresponds to the third harmonic, where the rope has three segments vibrating, affecting the wavelength and frequency calculations.
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06:28Equations for Transverse Standing Waves
Wave Equation for Harmonics
The wave equation for harmonics relates the length of the medium to the wavelength of the standing wave. For a rope fixed at both ends, the wavelength of the nth harmonic is given by λ = 2L/n. Understanding this equation helps calculate the wavelength and frequency of the second overtone, which is the third harmonic.
Recommended video:
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06:28Equations for Transverse Standing Waves
Related Practice
Textbook Question
A wire with mass 40.0 g is stretched so that its ends are tied down at points 80.0 cm apart. The wire vibrates in its fundamental mode with frequency 60.0 Hz and with an amplitude at the antinodes of 0.300 cm. What is the speed of propagation of transverse waves in the wire?
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Textbook Question
Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm. <IMAGE> Sketch the shape of the string at the end of 7.0 s.
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Textbook Question
A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the fundamental?
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Textbook Question
A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire is 0.400 m long and has a mass of 3.00 g. What is the frequency of its fundamental mode of vibration?
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Textbook Question
A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the fourth harmonic?
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