Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8...
Transcript of Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8...
![Page 1: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/1.jpg)
This is PHYS 1240 - Sound and Music
Lecture 8
Professor Patricia Rankin
Cell Phones silent
Clickers on
![Page 2: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/2.jpg)
Physics 1240 Lecture 8
Today: Standing waves. Waves on strings
Next time: Waves in pipes – Tyler!
physicscourses.colorado.edu/phys1240 (lecture notes, solutions)
Canvas Site: assignments, administration, grades
Homework – HW4 Due Wed February 12th 5pm
Homelabs – Hlab2 Due Monday Feb 10th 5pm
![Page 3: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/3.jpg)
Last lecture - Debrief
A (normal) mode is a motion where every point moves with the same frequency
𝑳 = λ/2 ;
= 2L
A node is a place where a mode has no motion
An anti-node is a place where a mode has maximum motion
(count to get # of mode)
𝑳 = λ
𝑳 = 3λ/2 ; = 2L/3
𝑳 = nλ/2 ; = 2L/n
![Page 4: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/4.jpg)
Can we summarize relations as an equation? Yes !
𝑣𝑡 = 𝑓𝑛𝑛=𝑓𝑛2𝐿
𝑛
𝑓𝑛 = 𝑛 ∙𝑣𝑡2𝐿
𝑛 = 1, 2, 3, 4, …
𝑳 = nλ/2 ; = 2L/n
![Page 5: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/5.jpg)
Velocity of Transverse Waves on a String
F=tv
tension (N)
mass/length (kg/m)
Book uses vs
But it is not the speed of sound in air!
![Page 6: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/6.jpg)
Vibrating Strings (handy formulae)
• For the 𝑛th harmonic,
𝐿 = 𝑛λ
2
• Recall: 𝑣 = 𝜆𝑓
⇒ 𝑓𝑛 = 𝑛𝑣𝑡2𝐿
• New formula: 𝑣𝑡 =𝑇
𝑚/𝐿=
𝐹
μ
𝑓𝑛 =𝑛
2𝐿
𝑇
𝑚/𝐿
tension
mass per
unit length
![Page 7: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/7.jpg)
What are the units of μ ?
A. m/s
B. kg
C. N
D. kg/m
E. m/s2
F=tv
CLICKER 8.1
![Page 8: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/8.jpg)
What are the units of μ ?
A. m/s
B. kg
C. N
D. kg/m
E. m/s2
F=tv
CLICKER 8.1 D
![Page 9: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/9.jpg)
What are the units of F?
A. m/s
B. kg
C. N
D. kg/m
E. m/s2
F=tv
CLICKER 8.2
![Page 10: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/10.jpg)
What are the units of F?
A. m/s
B. kg
C. N
D. kg/m
E. m/s2
F=tv
CLICKER 8.2 C
1N = 1 kg m/s2 ; N/(kg/m) = m2/s2
![Page 11: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/11.jpg)
If the tension is increased by a factor of 9
what happens to the speed of waves on a
string?
A. Goes up by a factor of 3
B. Goes up by a factor of 4.5
C. Goes up by a factor of 9
D. Goes up by a factor of 81
E. None of these / I don’t know
F=tv
CLICKER 8.3
![Page 12: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/12.jpg)
If the tension is increased by a factor of 9
what happens to the speed of waves on a
string?
A. Goes up by a factor of 3
B. Goes up by a factor of 4.5
C. Goes up by a factor of 9
D. Goes up by a factor of 81
E. None of these / I don’t know
F=tv
CLICKER 8.3 A
![Page 13: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/13.jpg)
If you increase tension by a factor of 4 …
A) The frequency of the fundamental doubles, all
other harmonics stay the same as they were
B) The frequency of every harmonic doubles
C) None of the frequencies change, the
wavelengths double
D) f1 goes up by 2, f2 by 4, (etc…)
E) Something else?
CLICKER 8.4
![Page 14: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/14.jpg)
If you increase tension by a factor of 4 …
A) The frequency of the fundamental doubles, all
other harmonics stay the same as they were
B) The frequency of every harmonic doubles
C) None of the frequencies change, the
wavelengths double
D) f1 goes up by 2, f2 by 4, (etc…)
E) Something else?
CLICKER 8.4 B
![Page 15: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/15.jpg)
A string vibrates with a fundamental frequency of 220 Hz.
Besides 220 Hz, which of the following are resonant
frequencies you might also observe?
i) 110 Hz
ii) 330 Hz
iii) 440 Hz
A: i only
B: ii only
C: iii only
D: i and ii
E: all three
CLICKER 8.5
![Page 16: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/16.jpg)
A string vibrates with a fundamental frequency of 220 Hz.
Besides 220 Hz, which of the following are resonant
frequencies you might also observe?
i) 110 Hz
ii) 330 Hz
iii) 440 Hz
A: i only
B: ii only
C: iii only
D: i and ii
E: all three
CLICKER 8.5 C
![Page 17: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/17.jpg)
A string on an instrument plays an A (440 Hz)
when plucked. If you lightly touch the string
½ way from one end, and then pluck, you are
mostly likely to hear…
A: Still 440 Hz
B: 220 Hz
C: 880 Hz
D: Something entirely different
CLICKER 8.6
![Page 18: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/18.jpg)
A string on an instrument plays an A (440 Hz)
when plucked. If you lightly touch the string
½ way from one end, and then pluck, you are
mostly likely to hear…
A: Still 440 Hz
B: 220 Hz
C: 880 Hz
D: Something entirely different
CLICKER 8.6C
![Page 19: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/19.jpg)
Octaves
When you increase frequencies by an octave you
double the frequency
Two octaves higher means an increase by a factor
of four
Three octaves higher is a factor of 8 (= 2x2x2 = 23 )
When things increase in this way (according to a
power) we have an example of an exponential
growth
![Page 20: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/20.jpg)
A string has a fundamental frequency f1.
The second mode has frequency f2 = 2f1, or one
octave higher.
Which mode is TWO octaves above f1?
A) f3 B) f4 C) f5
D) f8 E) ??
CLICKER 8.7
![Page 21: Cell Phones silent Clickers on - Physics · Cell Phones silent Clickers on. Physics 1240 Lecture 8 Today: Standing waves. Waves on strings Next time: Waves in pipes –Tyler! physicscourses.colorado.edu/phys1240](https://reader033.fdocuments.net/reader033/viewer/2022042418/5f34b204d8d76801793c8aa1/html5/thumbnails/21.jpg)
A string has a fundamental frequency f1.
The second mode has frequency f2 = 2f1, or one
octave higher.
Which mode is TWO octaves above f1?
A) f3 B) f4 C) f5
D) f8 E) ??
CLICKER 8.7 B