This preview shows pages 1–4. Sign up to view the full content.
HW 2: Physics 1B Spring 2010
C. M. Cooper, Teaching Assitant
W. Gekelman, Professor
April 16, 2010
Abstract
This hw covers all of chapter 15. Topics include standing waves in pipes and then a ton of
random things. These include sound wave velocity, pressure, intensity, interference, beats, and
doppler shifts. You should know the speed of sound in air at 20 C = 344 m/s.
1 Question 16.10: speed of sound with temperature
This problem involves taking ”a diﬀerential” then using it in a taylor series. These sorts of things
are goign to become more commonplace as you move forward. Starting at equation 16.10
v
=
r
γRT
M
(1)
dv
=
d
±
r
γRT
M
²
=
r
γR
M
dT
2
√
T
=
r
γR
M
dT
1
2
√
T
√
T
√
T
=
v
dT
2
T
(2)
now we use a ”ﬁrst order taylor expansion” which is the same as splitting the Δ
v
into
v
f

v
i
Δ
v
=
dv
dT
Δ
T
=
v
2
T
Δ
T
=
344
m/s
2
×
293
C
(1
C
) = 0
.
59
m/s
(3)
2 Question 16.25: Waves in Tubes
This problem is best done graphically and writing out the answer from the pictures. The most
important part of this problem is knowing the diﬀerence between the pressure nodes and the am
plitude nodes, and that they are
π/
2 out of phase (pressure nodes occur at amplitude antinodes
and vice versa). You can do this with formulas for
λ
n
if you know them but you still need to draw
the pics, here they are below.
For the fundamental, the displacement node is at 0.6 m and the pressure nodes (displacement
antinodes) are at 0 m and 1.20 m.
For the ﬁrst overtone (second harmonic), the displacement nodes are at 0.3 m and 0.9 m and
the pressure nodes are at 0 m, 0.6 m and 1.2 m.
For the second overtone (third harmonic), the displacement nodes are at 0.2 m 0.6 m and and
1.0 m and the pressure nodes are at 0 m, 0.4 m, 0.8 m and 1.2 m.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Figure 1: This is best done graphically
Figure 2: hey, hey, hey. goodbye.
For the fundamental, the displacement node is at 0 m and the pressure node (displacement
antinodes) is at 1.20 m.
For the ﬁrst overtone (second harmonic), the displacement nodes are at 0.0 m and 0.8 m and
the pressure nodes are at 0.4 m and 1.2 m.
For the second overtone (third harmonic), the displacement nodes are at 0.0 m 0.48 m and and
0.96 m and the pressure nodes are at 0.24 m, 0.72 m, and 1.2 m.
3 Question 16.32: a Can on a String
You’re going to be making a wave in one medium and converting it to another. Remember when
you see
μ
or
F
T
think
v
which if you have
λ
you can get anything
k,ω,f
. The question is though,
what do you do at the boundary? You might be tempted to match the velocities but what you
actually want is for them to resonate together, i.e. they have the same frequencies. This means
f
pipe
=
f
wire
. Subbing in for the
n
th
frequency of both gives
v
s
4
L
pipe
=
3
v
wire
2
L
wire
=
3
2
L
wire
s
F
m/L
wire
(4)
rearranging gives
L
pipe
=
L
wire
v
s
6
p
FL
wire
/m
=
.
85
×
344
6
p
4110
×
.
85
/.
00725
= 0
.
07
m
(5)
2
4 Question 16.43: How’d That Guy get There?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 05/12/2010 for the course PHYSICS 1B 318007220 taught by Professor Gekelman during the Spring '10 term at UCLA.
 Spring '10
 gekelman

Click to edit the document details