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Ch 15: Mechanical Waves
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 15: Mechanical WavesProblema 36b
Capitolo 15, Problema 36b

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?

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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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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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Percorso guidato
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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Percorso guidato
06:28
Equations 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.
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Percorso guidato
06:28
Equations for Transverse Standing Waves
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