{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p288_05_w11_nq

# p288_05_w11_nq - PAT 102/Physics 288/489 Winter 2011 L e c...

This preview shows pages 1–8. Sign up to view the full content.

PAT 102/Physics 288/489 Winter 2011 Lecture 5 Graphs Logs Cents

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Periodic Waves and Vibrations Waves and oscillations are characterized by – Frequency f – Period P (or sometimes T ) – Amplitude A – Wavelength (for waves) λ – Speed (for waves) v For simple harmonic motion v = " f = " / P P = 1/ f f ! Restoring force Inertia period
Examples of Simple Harmonic Motion Mass on a spring – Mass m and spring constant k Simple pendulum – Length L Vibrating stretched string – Tension T , length L and mass per unit length μ f = 1 2 ! k m f = 1 2 ! g L f = 1 2 L T μ Frequency is independent of the amplitude

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Galileo’s studies of Vibrations Realized that pendulums provide a good way of measuring time – Needed for his careful studies of motion – Ideas about timing probably influenced by his father and musician Vincenzo Galilei After age 70 and under house arrest, Galileo returns to pendulums, vibrations and music – Published results in a book: Discourses on two new sciences
Galileo’s Idea About Consonance Why are consonant musical intervals related to simple numerical ratios? Galileo’s argument: – Musical tones are associated with oscillations – Consonance occurs when the oscillations form a regular repeating pattern Interval Ratio Unison (prime) 1:1 Octave 2:1 Perfect fifth 3:2 Perfect fourth 4:3 Major third 5:4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Consonance of the Octave “Agreeable consonances are pairs of tones which strike the ear with a certain regularity. The first and most pleasing consonance is, therefore, the octave, for every pulse given to the tympanum by the lower string, the sharp string delivers two.” A 4 A 5 One cycle Two cycles The pulses are “in sync” every cycle of the A 4 oscillation and every other cycle of the A 5 oscillation 2:1 ratio
Consonance of the Fifth “The fifth, however, is characterized by its displaced beats, that is, by the interposition of two solitary beats of the upper, and one of the lower, between each case of simultaneous pulses. Moreover, these three are separated by time intervals one-half of that which separates simultaneous pulses from pulses of the upper string.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 30

p288_05_w11_nq - PAT 102/Physics 288/489 Winter 2011 L e c...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online