Physics Unit 10: Sound & Music
Number
Due
Assignment
HW 10-1
Mon 2/24
Read 12.1 and 12.2; (409) 2, 5, 6; (416) 1; (432) 3, 4; Supplemental 1, 2
HW 10-2
Tues 2/25
Read 12.3; (423) 1-4; (432) 8, 9**, 14, 18
HW 10-3
Wed 2/26
(427) 1, 2; (433) 25, 30, 31; Supplemental 3-6
HW 10-4
Thur 2/27
Read p.428-429; (433) 34, 35; Supplemental 7-9
MQ 10
Sun 3/02
There will be 8 questions for 12 points. Due Sunday night @midnight
(** Hint: see figure 1.3 on p.407)
Musical Instrument Lab: Tuesday 2/25 to Friday 2/28
(Don’t forget your group’s instrument!! “Perfect Attendance” is desired!!)
Test Monday March 3rd, 2014
Supplemental Problems
1. In which of these situations does the♭ Doppler Effect occur? (a) a
source of sound moves toward a listener; (b) a listener moves toward a
source of sound; (c) a listener and a source of sound move away from each
other; (d) a listener and a source of sound moved toward each other; (e) all
of these.
2. A car whooshes past you and makes a sound that changes pitch
slightly as it passes you. Explain why it makes a lower pitched sound as it
moves away from you.
3. Look at the table of the American Standard Scale. (a) Find an example
to show that successive notes are not separated by a fixed number of Hertz.
(b) Use an example to show that the frequencies of successive notes have a
fixed ratio.
4. (a) How many notes are there in an octave? (b) Still using the
American Standard Scale, describe the general relationship between the
frequencies of a note, one octave up from that note, and one octave down
from that note. (c) Explain why your ratio from 3b above has to be the
twelfth root of two♯.
5. The American Standard Scale is based on A4 being 440 Hz. The
Scientific Scale is based on middle C being 256 Hz. The Scientific Scale is
typically not used for musical purposes. Does the Scientific Scale follow
the same patterns that you found in questions 3 and 4? Use examples to
demonstrate.
6. A “perfect fifth” is based on two notes having a ratio of frequencies of
exactly 1.5. (a) Find two notes that have this ratio (or close to this ratio).
(b) By how many notes are these two apart? (c) Pick two other notes that
are separated by the same number of notes and see if they also have a ratio
of 1.5.
Aside: A scale with a fixed ratio between notes (like the two listed here) is
called a Chromatic Scale (also “well-tempered” and “even tempered”).
There are other scales (for instance, the Just Scale and the Pythagorean
Scale) that produce perfect fifths and other intervals more precisely, but
they have the disadvantage of not having a uniform ratio up and down the
musical spectrum.
Note
American
Standard Scale Scientific Scale
A
110.0 Hz
107.6 Hz
A♯ or B♭
116.5 Hz
114.0 Hz
B
123.5 Hz
120.8 Hz
C
130.8 Hz
128.0 Hz
C♯ or D♭
138.6 Hz
135.6 Hz
D
146.8 Hz
143.7 Hz
D♯ or E♭
155.6 Hz
152.2 Hz
E
164.8 Hz
161.3 Hz
F
174.6 Hz
170.9 Hz
F♯ or G♭
185.0 Hz
181.0 Hz
G
196.0 Hz
191.8 Hz
G♯ or A♭
207.7 Hz
203.2 Hz
A
220.0 Hz
215.3 Hz
A♯ or B♭
233.1 Hz
228.1 Hz
B
246.9 Hz
241.6 Hz
C
261.6 Hz
256.0 Hz
C♯ or D♭
277.2 Hz
271.2 Hz
D
293.7 Hz
287.4 Hz
D♯ or E♭
311.1 Hz
304.4 Hz
E
329.6 Hz
322.5 Hz
F
349.2 Hz
341.7 Hz
F♯ or G♭
370.0 Hz
362.0 Hz
G
392.0 Hz
383.6 Hz
G♯ or A♭
415.3 Hz
406.4 Hz
A
440.0 Hz
430.5 Hz
A♯ or B♭
466.2 Hz
456.1 Hz
B
493.9 Hz
483.3 Hz
C
523.3 Hz
512.0 Hz
C♯ or D♭
554.4 Hz
542.4 Hz
D
587.3 Hz
574.7 Hz
D♯ or E♭
622.3 Hz
608.9 Hz
E
659.3 Hz
645.1 Hz
F
698.5 Hz
683.4 Hz
F♯ or G♭
740.0 Hz
724.1 Hz
G
784.0 Hz
767.1 Hz
G♯ or A♭
830.6 Hz
812.7 Hz
A
880.0 Hz
861.1 Hz
7. The frequency of a turning fork can be determined if you trust a value for the
speed of sound. One method would involve a setup like in Figure 1. A long tube
open at both ends is submerged in a beaker of water, and the vibrating tuning fork
is placed near the top of the tube. The length of the air column, L, is adjusted by
moving the tube vertically. The sound waves generated by the fork are reinforced
when the length of the air column corresponds to one of the resonant frequencies
of the tube. The smallest value for L which generates resonance is 9.00 cm. (Use
345m/s as the speed of sound in air.)
(a) What is the frequency of the tuning fork?
(b) What is the value of L for the next two harmonics?
8. (a) In order to determine how much a galaxy is red-shifted or blue-shifted, is it
necessary to know the original frequency (color) of the galaxy? (b) In 1929 Edwin
Hubble observed that almost all galaxies are red-shifted. What could he conclude
from this observation?
9. Is the Big-Bang theory accepted by most scientists or is it still being worked
on?