109 lines
2.1 KiB
Plaintext
109 lines
2.1 KiB
Plaintext
#LyX 2.1 created this file. For more info see http://www.lyx.org/
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\lyxformat 474
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\begin_document
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\begin_header
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\textclass article
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\use_default_options true
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\maintain_unincluded_children false
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\language english
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\language_package default
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\inputencoding auto
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\fontencoding global
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\font_roman default
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\font_sans default
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\font_typewriter default
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\font_math auto
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\font_default_family default
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\use_non_tex_fonts false
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\font_sc false
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\font_osf false
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\font_sf_scale 100
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\font_tt_scale 100
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\graphics default
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\default_output_format default
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\output_sync 0
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\bibtex_command default
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\index_command default
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\paperfontsize default
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\use_hyperref false
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\papersize default
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\use_geometry false
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\use_package amsmath 1
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\use_package amssymb 1
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\use_package cancel 1
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\use_package esint 1
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\use_package mathdots 1
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\use_package mathtools 1
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\use_package mhchem 1
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\use_package stackrel 1
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\use_package stmaryrd 1
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\use_package undertilde 1
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\cite_engine basic
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\cite_engine_type default
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\biblio_style plain
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\use_bibtopic false
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\use_indices false
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\paperorientation portrait
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\suppress_date false
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\justification true
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\use_refstyle 1
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\index Index
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\shortcut idx
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\color #008000
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\end_index
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\secnumdepth 3
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\tocdepth 3
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\paragraph_separation indent
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\paragraph_indentation default
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\quotes_language english
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\papercolumns 1
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\papersides 1
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\paperpagestyle default
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\tracking_changes false
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\output_changes false
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\html_math_output 0
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\html_css_as_file 0
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\html_be_strict false
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\end_header
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\begin_body
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\begin_layout Standard
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\begin_inset Formula $K=\frac{\partial F}{\partial x}=S_{l}\frac{\partial p}{\partial x}=S_{l}\frac{\partial p}{\partial\rho}\frac{\partial\rho}{\partial x}=S_{l}c_{0}^{2}$
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Formula $\rho=\rho_{0}\frac{V_{0}}{V}$
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\end_inset
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,
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\begin_inset Formula $V=V_{0}+S_{l}x$
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Formula $\frac{\partial\rho}{\partial x}=-S_{l}\frac{\rho_{0}}{V_{0}}$
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\end_inset
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\end_layout
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\begin_layout Standard
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Such that
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\end_layout
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\begin_layout Standard
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\begin_inset Formula $K=-S_{l}^{2}\frac{\rho_{0}c_{0}^{2}}{V_{0}}=-S_{l}^{2}\frac{p_{0}}{\gamma V_{0}}$
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\end_inset
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\end_layout
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\end_body
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\end_document
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