PHYS207     Set 2 Assignment         Spring 2012

Chapter 7 RQ 11,12,13,15  Q 1,3  Ex. 1
Chapter 8 Q 3  Ex. 7 (why is Fig. 8.11 a bad example?)
Chapter 11 E1
Chapter 12 E5
Chapter 23 Q 2, 3  E2,3,4,8

1) Two supposedly identical strings in a piano (hit by the same hammer) are in fact mistuned by 10 cents.
What will be the beat frequency between the two fundamentals if the note is
a) A1 (55 Hz) 
b) A6 (1760 Hz)

c) The piano tuner reduced the beat rate in case b) to 2 Hz. What is now the mistuning (in cents) ?

2) a)  In a church, you notice a pipe about as tall  as you are, producing sound of fundamental frequency 100 Hz.
Is it an open-open or open-closed pipe? Explain your reasoning.

b) If the organ builder now changes the end of the pipe  from open to closed - or from closed to open - depending on  what you found in a), what will now be the new fundamental frequency, and what will be the frequency of the first overtone?

3) Compare the intervals contained in chords C4/E4/G4 and D4/F4/A4.
What is different? (Note: there is more to this than meets the eye ...).

 4) Determine the (main) beat rate in an equally tempered Major 3rd if the bottom tone has frequency of a) 220 Hz b) 1760 Hz

5) Determine what happens if you go
a) up 12 fifths then down 7 octaves
b) up 3 Major thirds then down 4 minor thirds

in both cases consider both the "just" tuning as well as Equal Temperament.

6)  Construct the deCaus tuning scheme
(start with perfect major thirds F-A-C#, then build three perfect
fifths upward from each of these three notes) and compare with equal
temperament.

7) 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).

(Note: this is much more precise than calculating RT from scratch.
It can also be turned around: calculate the absorption coefficient
(of the carpet, in this case) from the measured values of RT before and
after ... )
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Concepts to explain:
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Heisenberg Principle 

missing fundamental
timbre vs. Fourier spectrum, vibrato / tremolo
beats vs. difference tones, consonance and dissonance vs. small integer ratios
musical intervals, scales, chords, tuning(s) vs. temperament(s)

what are "soft reeds" and "hard reeds"

what are the differences between the sound of an open/open vs. an open/closed pipe

what happens to the sound of the pipe organ if the room temperature changes?

what are the consequences of the inharmonicity of real strings on the sound of

a) struck/plucked strings b) bowed strings

Explain why all large enough rooms have the same RT at high frequencies, and on what parameter does this value depend?