Physics of Sound 301
HOMEWORK ASSIGNMENT #9
Due Friday April 15, 2005
RMW refers to the textbook The Science of Sound, 3rd
Edition, by T.D. Rossing, F.R. Moore, & P.A. Wheeler
- Note that the schedule for final projects has been set-up.
Student presentations begin next week! Be sure to check the Final
projects web page for details of when you are presenting.
- RMW, page 223, exercise 2 and 4.
- Explain qualitatively how changes in bowing point and bowing speed
are related to changes in overall vibration amplitude for a bowed string.
Think carefully about how the bow and string must move at the same speed
when sticking at the bowing point. It may help to sketch how these changes
would alter figures 10.6 and 10.8 in RMW.
- Modification of old violins during the 19th-century included
replacement of gut strings by metal-wound or steel strings and
lengthening of the neck to increase string length. These factors, in
conjunction with the gradual rise of standard pitch for A4 from
approximately 420 Hz toward 440 Hz, result in the use of greater
string tension. Other things being equal, what would be the
percentage increase in tension for each of these cases:
What would be the overall increase in tension for all these changes together?
- change in the standard pitch of A4 from 415 to 440 Hz,
- increase in active string length from 32 to 33 cm, and
- replacment of gut strings with 10% heavier metal-wound strings.
- RMW, page 353, exercise 4.