Vibratory Motion and SoundLongmans, Green, 1882 - Broj stranica: 135 |
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Stranica 9
Joseph David Everett. of x with the same velocity , so that if x denote the distance travelled in time t we shall have x = vt , or t = 1 . V But from equation ( 4 ) , with y in place of x , we have y = a cos T 1 ( 2πt — € ) , that is , y ...
Joseph David Everett. of x with the same velocity , so that if x denote the distance travelled in time t we shall have x = vt , or t = 1 . V But from equation ( 4 ) , with y in place of x , we have y = a cos T 1 ( 2πt — € ) , that is , y ...
Stranica 41
... x the line which passes through the middle points of the paths of the particles , and taking any point in this line ... vt 2 , by equation ( 8 ) . As we pass from one particle to another , in the direction in which the waves travel , x ...
... x the line which passes through the middle points of the paths of the particles , and taking any point in this line ... vt 2 , by equation ( 8 ) . As we pass from one particle to another , in the direction in which the waves travel , x ...
Stranica 43
... vt - x 2 π , λ we have therefore but dy_dy do dy_ dx as dx dt do dx dy do do dť do dy.dy .. do dx at dx at ' = — 2π λ do and dt = 2 T U λ hence which agrees dy . dy .. v , : RELATION OF SLOPE TO VELOCIT Y. 43.
... vt - x 2 π , λ we have therefore but dy_dy do dy_ dx as dx dt do dx dy do do dť do dy.dy .. do dx at dx at ' = — 2π λ do and dt = 2 T U λ hence which agrees dy . dy .. v , : RELATION OF SLOPE TO VELOCIT Y. 43.
Stranica 47
... vt - x 2 by 0 , we may write the equations of the two undulations , on the as- sumption that λ is the same for both , Y1 = a cos 0 , y2 = b cos ( 0-4 ) , and the equation of the resultant undulation will be y = a cos + b cos ( 0-6 ) ...
... vt - x 2 by 0 , we may write the equations of the two undulations , on the as- sumption that λ is the same for both , Y1 = a cos 0 , y2 = b cos ( 0-4 ) , and the equation of the resultant undulation will be y = a cos + b cos ( 0-6 ) ...
Stranica 48
... ( vt - x 2 T λ −4 ) , where c and are independent both of x and t . This last equation evidently denotes a simple harmonic un- dulation of wave length a , velocity v and amplitude c . 56. On the supposition of a slight difference in the ...
... ( vt - x 2 T λ −4 ) , where c and are independent both of x and t . This last equation evidently denotes a simple harmonic un- dulation of wave length a , velocity v and amplitude c . 56. On the supposition of a slight difference in the ...
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amplitude antinode approximately axis beats called centre CHAPTER circle coefficient of elasticity component compound compression crank Crown 8vo curve cylinder denote described difference displacement distance Edition ellipse elliptic harmonic motion epoch equal equation extreme positions fixed force fork Hence History horizontal interval JOHN STUART MILL length LL.D lowest position Maps maximum mean value middle point musical nodes number of vibrations obtained opposite directions parallel parallelogram particle pendulum period of vibration perpendicular phase pipe pitch plane Plates Post 8vo pressure produce pulleys pulse quarter period R. A. PROCTOR ratio resultant revolving rhombus right angles round S. R. GARDINER S.H. motion side simple harmonic motion simple tones sin² slot sound square statical energy stationary straight line string tions toothed wheel tracing tube uniform circular motions velocity of propagation vertical vibrations per second vols vt-x wave-length Woodcuts