Chapter 11 E1
L2/L1 = f1/f2 = twelveth root of 2 = 1.06 => L2 = L1*f1/f2 = 275*1.06
= 291.5
this means that the u-shaped slide has to be moved by (291.5-275)/2
= 8.25 cm.
Chapter 12 E5
a) f=v/2L = 343/(2*0.42) = 408 Hz
b) F4 is 4 semitones below A4 which is 440 Hz in standard modern tuning.
So the f(F4) = 440/(twelveth root of two^4) = 440/(cube root of two)
= 349 Hz
c) The difference between a) and b) is due to the end corrections (note
that the end corrections at the mouth end are very difficult to calculate).
Chapter 14 E2 (is the solution given in Text correct?)
At first sight, you may think that they forgot to give you the original
frequency of the unison. But that is in fact not necessary:
f(beats) = f2-f1 => time (out of phase) = 1/(2*f(beats))
# of vibrations(until out of phase) = time(out of phase)/T1 (where
T1 = 1/f1)
putting the above together, we get:
# of vibrations(until out of phase) = 1/(2(f2/f1 - 1) = 1/(2*(1.0012
- 1)) = 417
Chapter 15 E1
f1 = v/4L = 343/(4*0.11) = 780 Hz compare 690 Hz
f3 = 3f1 = 2339 Hz (not 2239) compare 2610
f5 = 5f1 = 3898 Hz compare 3570
E2: graph shown in class
Chapter 16 E2
I have no idea what I was thinking when I assigned this one ...
Chapter 23 E2
(note: data for occupied wooden seats are not given, so we take occupied
upholstered seats. The difference is not large (e.g. absorption of persons
depends on whether they have coats or not, etc. ......)
40m=depth 20m=width 15=height
plywood walls: A=2*20*15*0.17 =102
plaster side walls and ceiling A=(2*40*15 + 40*20)*0.06 = 120
wood floor A=40*20*0.10 = 80
1100 wooden seats*0.02 = 22
550 wooden seats*0.02 +550 occupied seats*0.56 = 319
1100 occupied seats *0.56 = 616
RT(empty) = .161*40*20*15/(102+120+80+22) = 6 sec
RT(half full) = .161*40*20*15/(102+120+80+319) = 3.1 sec
RT(full) = .161*40*20*15/(102+120+80+616) = 2.1 sec
E3:
arrival time of direct sound = 20/344 = 58 ms
first reflection from ceiling = 2*sqrt(10^2+15^2)/344 = 105 ms
first reflection from side = 2*sqrt(10^2+10^2)/344 = 82 (24 ms after
direct sound)
E4:
plaster sides and new ceiling: A = 2*40*15*.06 +40*20*.76 = 680 - this
replaces the value of 120 in calculations of RT in E3 above
eg: RT(empty) = .161*40*20*15/(102+680+80+22) = 2.4 sec
RT(full) = .161*40*20*15/(102+680+80+319)
= 1.6 sec
E8: when absorption of surfaces can be neglected, the RT becomes
RT = .161 V/mV = .161/m independent of V
for air at 20 C 30% m = 0.136 at 8 kHz => RT = .161/.136
= 1.2 sec
Additional problem: A cathedral of volume 24,000 m^3 has RT=5 sec.
Determine the Reverberation Time at 500 Hz after 1,200 m^2
of painted concrete floor is covered with carpet (on pad).
RT = .161 V/A = 5 sec => A = .161 V/RT = .161*24000/5 = 773
new A = 773 + 1200*(.57 - .06) = 1385 => new RT = .161*24000/1385 =
2.8 sec
(Note: this is much more precise than calculating RT from scratch. It can also be turned around to calculate the absorption coefficient (of the carpet, in this case) from measured values of RT before and after ... Try this: "before painted concrete was covered, RT was 5 sec, after it was covered with carpet (different from above), RT became 3.2 sec. What is the absorption coefficient of that carpet? )
----------------------
Set 3 Part II:
what are "soft reeds" and "hard reeds"?
explain the difference between a partial and a formant. Frequency of which of the two will change if you inhale Helium?
Explain what will happen to pipe organ sound if the room temperature changes (this could be accompanied by a numerical problem: given that v(sound) = 331+0.6*T(Celsius), what temperature change would you consider acceptable?)
Explain why all large enough rooms have the same RT at high frequencies, and on what parameter does this value depend?
What is the difference between a WAV file, MP3 and MIDI file ?
-----------------------
NOTE: The term papers are due on Friday June 14. Please remember to
refer to ALL papers (including books and articles on WWW) that you used
in any way to prepare your paper. My favored way of referencing is actually
similar to that used in our Textbook: in the body of your paper, you refer
to a particular article by the last name of the (first) author, followed
by the year of publication (e.g. "as shown by Chaloupka 1998, ..."). At
the end of your paper, you have list of all references, alphabetically
ordered":
.....
Bernstein 1975, West Side Story, ...
Chaloupka 1998, Journal of Irreproducible Results, vol. 7, p. 324
Einstein 1905, Physical Review Vol 4, p. 45 ....
Gates 2002, URL = http://www.xxx.yyy/...
.....