R 7 will nger sent SECTION 7.2 (Classical Standing Waves) your answer to explain clearly why the w itself if we move from any point xo to Xo fixed). Show similarly what happens if w from any to to to + T. 7.1 . A string is oscillating with wave function t an y(x, t) = A sin kx cos ot her (7.118) e by om the ctly es. ed with A 3 cm, k = 0.2m rad/cm, and o For each of the times t = 0, 0.05, and 0.07 s, sketch the string for 0 x 10 cm. 10TT rad/s. A string is oscillating with wave fun 7.9 2.5 cm, k 1 form (7.118) but with A www.d 10TT rad/s. (a) Sketch two complete of the wave at each of the times t = t=0.1 s. (b) For a fixed value of x, (7.118) with respect to t to give the string velocity at any position x. Graph this function of x for each of the two times in K 22 A standing wave of the form (7.118) has amplitude 7.2 2 m, wavelength 10 m, and period T 2s. Write down the expression for y(x, t) E71 4 7.3 A string is clamped at the points x = 0 and x= 30 cm. It is oscillating sinusoidally with amplitude 2 cm, wavelength 20 cm, and frequency f = 40 Hz. Write an expression for its wave function y(x, t). SECTION 7.3 (Standing Waves in Quant Mechanics) 7.10 Prove that any complex number z = and y real) can be written as z re" real). Give expressions for x and y in te and vice versa. [Hint: Use Euler's form For the standing wave of Eq. (7.118) calculate the string's transverse velocity at any fixed position x. [That is, differentiate (7.118) with respect to t, treat- ing x as a constant.] At certain times the string's dis- placement is zero for all x, and an instantaneous 7.4 7.11 (a) Show for any complex numbe that z2zz where z = x - iy is conjugate of z. (b) Hence, prove the snapshot of the string would show no wave at all. and indicate. with
R 7 will nger sent SECTION 7.2 (Classical Standing Waves) your answer to explain clearly why the w itself if we move from any point xo to Xo fixed). Show similarly what happens if w from any to to to + T. 7.1 . A string is oscillating with wave function t an y(x, t) = A sin kx cos ot her (7.118) e by om the ctly es. ed with A 3 cm, k = 0.2m rad/cm, and o For each of the times t = 0, 0.05, and 0.07 s, sketch the string for 0 x 10 cm. 10TT rad/s. A string is oscillating with wave fun 7.9 2.5 cm, k 1 form (7.118) but with A www.d 10TT rad/s. (a) Sketch two complete of the wave at each of the times t = t=0.1 s. (b) For a fixed value of x, (7.118) with respect to t to give the string velocity at any position x. Graph this function of x for each of the two times in K 22 A standing wave of the form (7.118) has amplitude 7.2 2 m, wavelength 10 m, and period T 2s. Write down the expression for y(x, t) E71 4 7.3 A string is clamped at the points x = 0 and x= 30 cm. It is oscillating sinusoidally with amplitude 2 cm, wavelength 20 cm, and frequency f = 40 Hz. Write an expression for its wave function y(x, t). SECTION 7.3 (Standing Waves in Quant Mechanics) 7.10 Prove that any complex number z = and y real) can be written as z re" real). Give expressions for x and y in te and vice versa. [Hint: Use Euler's form For the standing wave of Eq. (7.118) calculate the string's transverse velocity at any fixed position x. [That is, differentiate (7.118) with respect to t, treat- ing x as a constant.] At certain times the string's dis- placement is zero for all x, and an instantaneous 7.4 7.11 (a) Show for any complex numbe that z2zz where z = x - iy is conjugate of z. (b) Hence, prove the snapshot of the string would show no wave at all. and indicate. with
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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I have written down a y(x,t) for the given values, but I think that I am not supposed to solve for the problem and then sketch. Am I supposed to solve the y(x,t) for the problem? Before I sketch? The problem is #7.1
![R 7
will
nger
sent
SECTION 7.2 (Classical Standing Waves)
your answer to explain clearly why the w
itself if we move from any point xo to Xo
fixed). Show similarly what happens if w
from any to to to + T.
7.1
. A string is oscillating with wave function
t an
y(x, t)
= A sin kx cos ot
her
(7.118)
e by
om
the
ctly
es.
ed
with A 3 cm, k = 0.2m rad/cm, and o
For each of the times t = 0, 0.05, and 0.07 s, sketch
the string for 0 x 10 cm.
10TT rad/s.
A string is oscillating with wave fun
7.9
2.5 cm, k
1
form (7.118) but with A
www.d
10TT rad/s. (a) Sketch two complete
of the wave at each of the times t =
t=0.1 s. (b) For a fixed value of x,
(7.118) with respect to t to give the string
velocity at any position x. Graph this
function of x for each of the two times in
K
22
A standing wave of the form (7.118) has amplitude
7.2
2 m, wavelength 10 m, and period T 2s. Write
down the expression for y(x, t)
E71 4
7.3 A string is clamped at the points x = 0 and
x= 30 cm. It is oscillating sinusoidally with amplitude
2 cm, wavelength 20 cm, and frequency f = 40 Hz.
Write an expression for its wave function y(x, t).
SECTION 7.3 (Standing Waves in Quant
Mechanics)
7.10 Prove that any complex number z =
and y real) can be written as z re"
real). Give expressions for x and y in te
and vice versa. [Hint: Use Euler's form
For the standing wave of Eq. (7.118) calculate the
string's transverse velocity at any fixed position x.
[That is, differentiate (7.118) with respect to t, treat-
ing x as a constant.] At certain times the string's dis-
placement is zero for all x, and an instantaneous
7.4
7.11 (a) Show for any complex numbe
that z2zz where z = x - iy is
conjugate of z. (b) Hence, prove the
snapshot of the string would show no wave at all.
and indicate. with](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81ed2a7d-ef58-4ac0-a29f-af1e2992bb8e%2Ff935fa8f-e551-4e5e-8bb5-4c2188317ec0%2Fv5gz1k.jpeg&w=3840&q=75)
Transcribed Image Text:R 7
will
nger
sent
SECTION 7.2 (Classical Standing Waves)
your answer to explain clearly why the w
itself if we move from any point xo to Xo
fixed). Show similarly what happens if w
from any to to to + T.
7.1
. A string is oscillating with wave function
t an
y(x, t)
= A sin kx cos ot
her
(7.118)
e by
om
the
ctly
es.
ed
with A 3 cm, k = 0.2m rad/cm, and o
For each of the times t = 0, 0.05, and 0.07 s, sketch
the string for 0 x 10 cm.
10TT rad/s.
A string is oscillating with wave fun
7.9
2.5 cm, k
1
form (7.118) but with A
www.d
10TT rad/s. (a) Sketch two complete
of the wave at each of the times t =
t=0.1 s. (b) For a fixed value of x,
(7.118) with respect to t to give the string
velocity at any position x. Graph this
function of x for each of the two times in
K
22
A standing wave of the form (7.118) has amplitude
7.2
2 m, wavelength 10 m, and period T 2s. Write
down the expression for y(x, t)
E71 4
7.3 A string is clamped at the points x = 0 and
x= 30 cm. It is oscillating sinusoidally with amplitude
2 cm, wavelength 20 cm, and frequency f = 40 Hz.
Write an expression for its wave function y(x, t).
SECTION 7.3 (Standing Waves in Quant
Mechanics)
7.10 Prove that any complex number z =
and y real) can be written as z re"
real). Give expressions for x and y in te
and vice versa. [Hint: Use Euler's form
For the standing wave of Eq. (7.118) calculate the
string's transverse velocity at any fixed position x.
[That is, differentiate (7.118) with respect to t, treat-
ing x as a constant.] At certain times the string's dis-
placement is zero for all x, and an instantaneous
7.4
7.11 (a) Show for any complex numbe
that z2zz where z = x - iy is
conjugate of z. (b) Hence, prove the
snapshot of the string would show no wave at all.
and indicate. with
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