大学物理 英文版 课件lu-Chap13&14-waves
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Chapter 13&14 Waves
1. Simple Harmonic Waves
2. Wave Equation 3. Energy and Power of Waves 4. Interference of Waves 5. Standing Waves 6. The Doppler Effect
The feature of wave’s propagation:
Explanations:
(1)A wave means that oscillatory state propagates with time. It does not mean the particles of medium move forward with wave. (2) Particles of the medium oscillate only around their corresponding equilibrium positions.
The velocity of particle oscillating u :
Oscillating velocity of particle at position x
2π
Oscillating Equ. of B: y 3 cos( 4 t ) Wave function about origin B:
x y 3 cos[ 4 ( t ) ] 20 13 13 (3) yC 3 cos 4 ( t ) 3 cos( 4t ) 20 5 9 9 y D 3 cos 4 ( t ) 3 cos( 4t ) 20 5
waves The direction of oscillation of medium elements is parallel to the direction of the wave’s travel, the motion is said to be longitudinal, and the wave is said to be a longitudinal wave.
then 2 x
(3) For varying t and x, it relates to the propagation of wave. y wave pattern at t+t
o
wave pattern at t
x x
x
v
x v t
If the wave moves along -x axis, then
The wave speed (P328): To ensure the wave form retaining, the phase in the above equations gives that its displacement must remain a constant: kx t o constant Taking its derivative,
13-1 Types of Waves
(P327)
1. Transverse waves The direction of oscillation of medium elements is perpendicular to the direction of travel of the wave.
Conditions of a mechanical wave: 1. A wave source 2. Medium in which a mechanical wave propagates. Simple harmonic wave: The wave source is at SHM, and the medium elements that the wave passes in medium are also at SHM.
For a source of SH oscillation with , the traveling in + x direction with & oscillating // y, no absorption in the medium (A for all elements) y (t ) Acos(t ) o 0 x ' t y P ( t ) A cos[ ( t t ' ) 0 ]
The wave speed on a stretched string (P328): Based on the description in P328, we have:
/
The speed of a wave along a stretched ideal string depends only on the tension and linear density of the string and not on frequency of the wave. The frequency of wave is fixed entirely by whatever generates the wave. The wavelength of the wave is then fixed by / f .
D( x , t ) DM sin( kx m t ) (See P334)
y ( x , t ) A sin[ 2 (
x
f t ) o ]
All waves in which the variables x and t enter in combination kx t are traveling waves.
k T Wave speed is the phase speed distance of an oscillatory state propagating in a unit-time or one wavelength per period.
dx dt k
f
x (1) y 3 cos 4 ( t ) Solution: 20 5 (2) y B 3 cos 4 ( t ) 20 20 10 m 2 Hz or Q f f 2 2
8m
C
B A
5m
9mБайду номын сангаас
D
x
2π AB 5 π 10
The physical meaning of wave equation:
(1) Fixed x, corresponding to the oscillating curve of medium element at position x, i.e. y(t, xo).
y
o
A T
t
(2) Fixed t, corresponding to the y-x curve at to.
Both a transverse wave and a longitudinal wave are said to be traveling waves because they both travel from one point to another.
13-2 Creation of Waves and Propagation
f
T
f times
f
1 f T
(4) 2 k , k
(where k is angular wave number)
Same phase points, phase difference is
2
2
Math’s expression of traveling waves (P332):
The characteristic quantities of wave: (1) The wavelength of a wave is the distance between repetitions of the wave shape, their phase difference is 2. (2) The T or f are the T or f of wave source, respectively. (3) Wave speed is the phase speed . The distance of an oscillatory state propagating in a unit-time, in one T, is the wave moves a distance of —— wavelength, so
y x1 A o
x2
x
At t0, the phase of element x2 is behind of x1:
[ (t
x2
) 0 ] [ (t
x1
) 0 ] 2
x2 x1
x x2 x1 : wave-path difference。
y ( x, t ) A cos[ (t
x
t x y ( x , t ) A cos[2 ( ) o ] T x y ( x, t ) A cos[2 ( ft ) o ]
) o ]
y ( x, t ) A cos(t kx o )
(3) When the source of wave finishes a complete oscillation, it forms an entire wave in its surrounding medium. (3) Later oscillatory particles always repeat oscillations that earlier ones did.
Example:
A SH wave travels in -x direction with speed =20m/s as Fig.If y A ( t ) 3 cos 4t , (1) write the equation for it about origin A;(2) how about origin B; (3) write oscillating equation of points C and D.
y
o x
P
x
y P (t ) A cos[ (t ) 0 ]
x
Note: The origin O can be arbitrary (may not be the source of wave). For different O, the expression for same wave is different.
The consistent forms with our book should be:
y ( x, t ) A sin[ ( t ) o ]
t y ( x , t ) A sin[ 2 ( ) o ] T
x
x
y ( x , t ) A sin(kx t o ) In general, wave function of an arbitrary shape of traveling wave has a form:
y
y P (t ) A cos[ (t ) 0 ]
x
o x
P
x
Note: the meaning of minus sign before x.
Using relationships: 2π 2π f T and k 2π T
Neglecting the subscript P, we have equivalent expressions for SH wave equation:
1. Simple Harmonic Waves
2. Wave Equation 3. Energy and Power of Waves 4. Interference of Waves 5. Standing Waves 6. The Doppler Effect
The feature of wave’s propagation:
Explanations:
(1)A wave means that oscillatory state propagates with time. It does not mean the particles of medium move forward with wave. (2) Particles of the medium oscillate only around their corresponding equilibrium positions.
The velocity of particle oscillating u :
Oscillating velocity of particle at position x
2π
Oscillating Equ. of B: y 3 cos( 4 t ) Wave function about origin B:
x y 3 cos[ 4 ( t ) ] 20 13 13 (3) yC 3 cos 4 ( t ) 3 cos( 4t ) 20 5 9 9 y D 3 cos 4 ( t ) 3 cos( 4t ) 20 5
waves The direction of oscillation of medium elements is parallel to the direction of the wave’s travel, the motion is said to be longitudinal, and the wave is said to be a longitudinal wave.
then 2 x
(3) For varying t and x, it relates to the propagation of wave. y wave pattern at t+t
o
wave pattern at t
x x
x
v
x v t
If the wave moves along -x axis, then
The wave speed (P328): To ensure the wave form retaining, the phase in the above equations gives that its displacement must remain a constant: kx t o constant Taking its derivative,
13-1 Types of Waves
(P327)
1. Transverse waves The direction of oscillation of medium elements is perpendicular to the direction of travel of the wave.
Conditions of a mechanical wave: 1. A wave source 2. Medium in which a mechanical wave propagates. Simple harmonic wave: The wave source is at SHM, and the medium elements that the wave passes in medium are also at SHM.
For a source of SH oscillation with , the traveling in + x direction with & oscillating // y, no absorption in the medium (A for all elements) y (t ) Acos(t ) o 0 x ' t y P ( t ) A cos[ ( t t ' ) 0 ]
The wave speed on a stretched string (P328): Based on the description in P328, we have:
/
The speed of a wave along a stretched ideal string depends only on the tension and linear density of the string and not on frequency of the wave. The frequency of wave is fixed entirely by whatever generates the wave. The wavelength of the wave is then fixed by / f .
D( x , t ) DM sin( kx m t ) (See P334)
y ( x , t ) A sin[ 2 (
x
f t ) o ]
All waves in which the variables x and t enter in combination kx t are traveling waves.
k T Wave speed is the phase speed distance of an oscillatory state propagating in a unit-time or one wavelength per period.
dx dt k
f
x (1) y 3 cos 4 ( t ) Solution: 20 5 (2) y B 3 cos 4 ( t ) 20 20 10 m 2 Hz or Q f f 2 2
8m
C
B A
5m
9mБайду номын сангаас
D
x
2π AB 5 π 10
The physical meaning of wave equation:
(1) Fixed x, corresponding to the oscillating curve of medium element at position x, i.e. y(t, xo).
y
o
A T
t
(2) Fixed t, corresponding to the y-x curve at to.
Both a transverse wave and a longitudinal wave are said to be traveling waves because they both travel from one point to another.
13-2 Creation of Waves and Propagation
f
T
f times
f
1 f T
(4) 2 k , k
(where k is angular wave number)
Same phase points, phase difference is
2
2
Math’s expression of traveling waves (P332):
The characteristic quantities of wave: (1) The wavelength of a wave is the distance between repetitions of the wave shape, their phase difference is 2. (2) The T or f are the T or f of wave source, respectively. (3) Wave speed is the phase speed . The distance of an oscillatory state propagating in a unit-time, in one T, is the wave moves a distance of —— wavelength, so
y x1 A o
x2
x
At t0, the phase of element x2 is behind of x1:
[ (t
x2
) 0 ] [ (t
x1
) 0 ] 2
x2 x1
x x2 x1 : wave-path difference。
y ( x, t ) A cos[ (t
x
t x y ( x , t ) A cos[2 ( ) o ] T x y ( x, t ) A cos[2 ( ft ) o ]
) o ]
y ( x, t ) A cos(t kx o )
(3) When the source of wave finishes a complete oscillation, it forms an entire wave in its surrounding medium. (3) Later oscillatory particles always repeat oscillations that earlier ones did.
Example:
A SH wave travels in -x direction with speed =20m/s as Fig.If y A ( t ) 3 cos 4t , (1) write the equation for it about origin A;(2) how about origin B; (3) write oscillating equation of points C and D.
y
o x
P
x
y P (t ) A cos[ (t ) 0 ]
x
Note: The origin O can be arbitrary (may not be the source of wave). For different O, the expression for same wave is different.
The consistent forms with our book should be:
y ( x, t ) A sin[ ( t ) o ]
t y ( x , t ) A sin[ 2 ( ) o ] T
x
x
y ( x , t ) A sin(kx t o ) In general, wave function of an arbitrary shape of traveling wave has a form:
y
y P (t ) A cos[ (t ) 0 ]
x
o x
P
x
Note: the meaning of minus sign before x.
Using relationships: 2π 2π f T and k 2π T
Neglecting the subscript P, we have equivalent expressions for SH wave equation: