wave motion - leibniz · wave motion. waves. condition: elastic media-taut string, spring...
TRANSCRIPT
![Page 1: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/1.jpg)
Wave motion
![Page 2: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/2.jpg)
Waves
![Page 3: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/3.jpg)
Condition: elastic media
-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc.
![Page 4: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/4.jpg)
![Page 5: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/5.jpg)
![Page 6: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/6.jpg)
Wave pulse
![Page 7: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/7.jpg)
x
f(x)t=0
vr
s
f(x-vt)
vr
s
f(x) t=0f(x+vt)
x
Traveling wave pulse
![Page 8: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/8.jpg)
Wave – like motion of a worm
![Page 9: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/9.jpg)
![Page 10: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/10.jpg)
![Page 11: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/11.jpg)
== xλπ2
sinA0)ty(x,
−= )vtx(2
sinAt)y(x,λπ
λ
2πk =Angular wave number:
ωttT2π
tλ/v2π
vtλ
2π ===
vr
( )ϕ+−= ωtkxsinAt)y(x,
max
vλ 1
T & Tλ
v =⋅→== ff
kω
v =
=A
![Page 12: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/12.jpg)
SuperpositionLinearity
![Page 13: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/13.jpg)
![Page 14: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/14.jpg)
Reflection of wave pulse
Open endFixed end
![Page 15: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/15.jpg)
inverted
uninverted
![Page 16: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/16.jpg)
Standing waves
2λ
![Page 17: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/17.jpg)
![Page 18: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/18.jpg)
Standing waves
( )kx-ωtAcost)(x,y1 = ( )kxωtAcost)(x,y2 +=
Standing wave: t)(x,yt)(x,yt)y(x, 21 +=
( ) ( )kxcosωtAcos2t)y(x, =
( ) ( ) /kxsinωtAsin2t)y(x, : / =ϕ
![Page 19: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/19.jpg)
Harmonics
fixed
L2λ1 =
Lλ L2λ
2 22 =→=⋅
3L
2λ L2λ
3 33 ⋅=→=⋅
4L
2λ L2λ
4 44 ⋅=→=⋅
λ
v=f
2Lv
λ
v
11 ==f
12
2 22Lv
2λ
vff ⋅=⋅==
13
3 32Lv
3λ
vff ⋅=⋅== 1n n ff ⋅=
![Page 20: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/20.jpg)
L
L2λ1 =
22L
λ2 =
32L
λ3 =
2Lv
λ
v
11 ==f
12
2 22Lv
2λ
vff ⋅=⋅==
13
3 32Lv
3λ
vff ⋅=⋅==
Open ends
1n n ff ⋅=
![Page 21: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/21.jpg)
Open endFixed end
L
4Lλ L4λ
11 =→=
34L
λ L4λ
3 22 =→=⋅
4Lv
λ
v
11 ==f
4Lv
3λ
v
22 ⋅==f
54L
λ L4λ
5 33 =→=⋅
4Lv
5λ
v
33 ⋅==f
1n 1)-n2( ff ⋅=
![Page 22: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/22.jpg)
![Page 23: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/23.jpg)
Ultrasound
![Page 24: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/24.jpg)
Beat frequency
![Page 25: Wave motion - Leibniz · Wave motion. Waves. Condition: elastic media-Taut string, spring (slinky)-Water surface, fluid-Solid state -Gas-Etc. Wave pulse. x t=0 f(x) v r s f(x-vt)](https://reader034.vdocuments.pub/reader034/viewer/2022043022/5f3e36f235fd0f376d6fe5d6/html5/thumbnails/25.jpg)
Doppler-effect
Sound source: at restObserver: moving at v
±=s
o vv
1ff
Sound source: moving at v Observer: at rest
=
s
o
vv
1
ff
m
±=
s
2
s
1
o
vv
1
vv
1ff
mSound source: moving at v2Observer: moving at v1