{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p288_05_w11 - PAT 102/Physics 288/489 Winter 2011 L e c tu...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
PAT 102/Physics 288/489 Winter 2011 Lecture 5 Graphs Logs Cents
Image of page 1

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

View Full Document Right Arrow Icon
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
Image of page 2
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
Image of page 3

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

View Full Document Right Arrow Icon
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
Image of page 4
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
Image of page 5

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

View Full Document Right Arrow Icon
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
Image of page 6
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. Thus the effect of the fifth is to produce a tickling of the eardrum, so that its gentleness is modified by sprightliness, giving the impression simultaneously of a gentle kiss and a bite.” A 4 Two cycles E 5 Three cycles 3:2 ratio
Image of page 7

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

View Full Document Right Arrow Icon
The Major Triad The major triad is a three note chord with a major third and a perfect fifth – The frequency ratios are f 2 / f 1 = 5/4 (major third) f 3 / f 1 = 3/2 (perfect fifth) – This can be expressed as f 1 : f 2 : f 3 = 4 : 5 : 6
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern