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
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)
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Previous Answers
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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
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2
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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.](https://content.bartleby.com/qna-images/question/7411e0a7-b731-43bf-a9b1-02a9a2969652/0827b021-ddd0-4fd1-bc56-c732eae1faab/r625ugl_processed.png)
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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