MUSIC HW: *ANSWERS*

l. A
group of tones that have regular wave patterns is:

*MUSIC*

2.
Sounds with an irregular wave pattern are called: *NOISE*

3.
Identify three properties of musical tones that can be distinguished by the
human ear.

a.
the frequency of the sound wave: * PITCH (Hz)*

the
amplitude of the sound wave: * LOUDNESS (DECIBEL)*

the
tone's distinct sound: *(QUALITY )*

1.
State what is meant by the fundamental frequency and overtone of a musical
tone:

* Fundamental: Main note, usually the
lowest, corresponding to the longest resonant wavelength. Overtones: harmonics,
or other notes made by the object vibrating a different way. Usually a whole
number multiple of the fundamental.*

5.
Identify the four classes of musical instruments and give at least one example
of each.

is
called

a.*
STRING: (node<->node) guitar, violin, piano*

b. *CLOSED
PIPE (node<->antinode), reed instruments: sax, clarinet, oboe, etc…*

c. * OPEN PIPE (antinode<->antinode)
brass? Flute, tuba, trumpet, etc..*

d. *2dimensional
(PERCUSSION)---- drum, etc…*

* *

6.
Explain the function of a vibrator and a resonator in musical instrument.

*The
thing that vibrates is the driving force…. the reed, you mouth, the pick, the
hammer, etc…. if it does it correctly it will cause the object to resonate at
its natural frequency…. The air in a tube or pipe, or the string, or the drum
head, etc..*

7.
The pitch of one string on your guitar is too low. What will you do to correct
it? Why

* You could shorten the string (shorter
wavelength=higher frequency) OR make it thinner or tighter ( faster speed, same
wavelength = higher frequency)*

*F
is the lowest note… the long wavelength, 1 is the first overtone (f1=2f0), 2 is
the 2 ^{nd} overtone ( f2=3 f0)*

* *

PROBLEMS: (Sec 13-3,13-4)

1) On a piano, the note
middle C has a fundamental frequency of 264 Hz. What is the second harmonic (1^{st}
overtone) of this note?

*Piano=string….. 1 ^{st} overtone is 2 * f0 = 528
Hz…*

*WL0= 2/1 L , WL1= 2/2 L
so f1 = 2*f0*

2) If the piano wire in item
one is 66 cm long, what is the wavelength of the sound? What is the speed of
sound?

*WL0 for the fundamental
is 2*.66 cm = 1.32 meters. For the first overtone WL1=.66m*

*V= WL*f = 1.32 * 264
= 348.48 m/second*

3) A piano tuner using a 392
Hz tuning fork to tune the wire for G natural hears four beats per second. What
are the two possible frequencies of vibration of this piano wire?

* The piano wire could be at 396 Hz or at
388 Hz.*

4) In a clarinet, the reed
end acts as a closed, and the first hole acts as an open. What is the
wavelength of the fundamental and the first two overtones as compared to the
length of the pipe? What are the frequencies?

*WL0 = 4 L , WL1 = 4/3 L , WL2 = 4/5 L*

* f0= V/ WL0 , f1 =3 f0 , f2 = 5 f0 etc…*

5) A .2 m long organ pipe is
closed at one end. What is its fundamental frequency when the temperature of
the air is 35 degrees Celsius? What are the frequencies of the first two
overtones?

* WL0 = 4 L = 4 * .2 = .8 meters. The v of
sound = 331 + .6 * °C = 331 +.6*35=352 m/s*

* F0 = V/WL0 = 352/.8 = 440 Hz (concert
A). *

*F1 = 3F0 (for a closed
pipe) = 1320 Hz, F2 = 5F0=2200 Hz*

* *

6) Mr T is singing an A note
at 440 Hz. His voice isn’t so pure, and he has an strong overtone at 880 Hz and
a weak (1/4 amplitude of the fundamental) at 660 Hz.

Draw each wave. (Hint use
graphing calculator?!)

*Y1= 1* sin (440x), Y2 =
.8* sin (880x), Y3= .25 * sin (660x)*

Draw what the superposition
of the waves would look like:

*Y= 1* sin (440x) + .8* sin (880x) + .25 *
sin (660x)*

*** Honors:

Find the fundamental and
overtones that would match this: (Fourier analysis)

*You should be able to
tell that there are 3 waves added together, and you see two complete patterns.*

*The lowest frequency
(longest wavelength) is the strongest, and the other shorter ones are a bit
weaker. But one of them is 180degrees out of phase! -sin*

* *

*So maybe:*

* -1*sin X + ½ * sin
2x + ¼ * sin 4x*