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Find the three longest wavelengths (call them A₁, A₂, and A3) that "fit" on the string, that is, those that satisfy the boundary conditions at z = 0 and L. These longest wavelengths have the lowest frequencies. Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas. ▸ View Available Hint(s) A₁, A2, A3 = Submit Part D - ΓΙ ΑΣΦ 3 ? The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength ₁ Find the frequency f; of the th normal mode. Express f; in terms of its particular wavelength X, and the speed of propagation of the wave v.

Find the three longest wavelengths (call them A₁, A₂, and A3) that "fit" on the string, that is, those that satisfy the boundary conditions at z = 0 and L. These longest wavelengths have the lowest frequencies. Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas. ▸ View Available Hint(s) A₁, A2, A3 = Submit Part D - ΓΙ ΑΣΦ 3 ? The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength ₁ Find the frequency f; of the th normal mode. Express f; in terms of its particular wavelength X, and the speed of propagation of the wave v.

Modern Physics
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter6: Quantum Mechanics In One Dimension
Section: Chapter Questions
Problem 24P
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Find the three longest wavelengths (call them A₁, A₂, and A3) that "fit" on the string, that is, those that satisfy the boundary conditions at z = 0 and z = L. These longest wavelengths have the lowest frequencies. Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas. ► View Available Hint(s) A₁, A2, A3 = Submit Part D fi= Submit The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength Xi- Find the frequency f; of the ith normal mode. Express f; in terms of its particular wavelength X; and the speed of propagation of the wave v. ▸ View Available Hint(s) [5] ΑΣΦ | α ΕΠΙ ΑΣΦΑ VO V A β γ π P 8 o € Previous Answers Σ Φ Ψ Ω n T Ф φ www. 0 K ? E 2 χ Χ Ψ @ ? μ
Transcribed Image Text:Find the three longest wavelengths (call them A₁, A₂, and A3) that "fit" on the string, that is, those that satisfy the boundary conditions at z = 0 and z = L. These longest wavelengths have the lowest frequencies. Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas. ► View Available Hint(s) A₁, A2, A3 = Submit Part D fi= Submit The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength Xi- Find the frequency f; of the ith normal mode. Express f; in terms of its particular wavelength X; and the speed of propagation of the wave v. ▸ View Available Hint(s) [5] ΑΣΦ | α ΕΠΙ ΑΣΦΑ VO V A β γ π P 8 o € Previous Answers Σ Φ Ψ Ω n T Ф φ www. 0 K ? E 2 χ Χ Ψ @ ? μ
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--- **Part E** Find the three lowest normal mode frequencies \( f_1, f_2, \) and \( f_3 \). Express the frequencies in terms of \( L, v, \) and any constants. List them in *increasing order*, separated by commas. **[Input Box]** \[ f_1, f_2, f_3 = \] **[Buttons]** - Submit - Request Answer This section asks for the calculation of normal mode frequencies using given variables. Ensure to arrange your answers from lowest to highest.
Transcribed Image Text:--- **Part E** Find the three lowest normal mode frequencies \( f_1, f_2, \) and \( f_3 \). Express the frequencies in terms of \( L, v, \) and any constants. List them in *increasing order*, separated by commas. **[Input Box]** \[ f_1, f_2, f_3 = \] **[Buttons]** - Submit - Request Answer This section asks for the calculation of normal mode frequencies using given variables. Ensure to arrange your answers from lowest to highest.
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