PHY138 – Waves, Lecture 5Today’s overview • Standing Waves • Harmonics • Beats
Reading Assignment • Please read the following from Serway and Jewett before class on Wednesday: Chapter 24, Sections 24.3, 24.7 and 24.9, and Context 7, pg. 896-897. Only the concepts of 24.3 are important, not the equations. • A Web-CT quiz is due Wednesday morning, which tests your basic familiarity with Chapter 24 and 25 assigned reading.
Written Homework The assignment due on Monday, November 29 at 5:00 PM is now available online. It includes problems from Chapter 14 and one from Chapter 24.
Some Announcements: • Calculator hint: “Exp” key stands for “times 10 to the power”. ie, to type 10-3, type 1 Exp (-) 3, not 10 Exp (-) 3. (the latter will be interpreted as 10×10-3=10-2 !) • Friday Tutorials Representative Assembly: this Friday, noon-1:00PM, MP713. • New medical technique to help stroke victims: ultrasound. Sound waves can dissolve brain blockages. (J.P. Polak, New England Journal of Medicine v.351 n.21, pg. 2154, Nov. 18 2004)
Doppler Effect sign conventions • Serway and Jewett say “A positive value is used for motion of the observer or the source toward the other.” • Other texts say: “A positive value is used for motion to the right, where the source is located to the right of the observer.”
Some results of superposition • 14.2: Two waves, same frequency, same direction, diffferent phase: Interference • 14.3-5: Two waves, same frequency, opposite direction: Standing Wave • 14.6 Two waves, same direction, slightly different frequency: Beats
Harmonic frequencies Transverse standing wave on a string clamped at both ends: there are nodes in displacement at both ends. Standing sound wave in a tube open at both ends: there are nodes in pressure both ends.
a Quiz 1 b • A string is clamped at both ends and plucked so creates a standing wave. Define upward motion to be positive velocities. When the string is in position b, the instantaneous velocity of points along the string • 1. is zero everywhere • 2. is positive everywhere • 3. is negative everywhere • 4. depends on location c
a Quiz 2 b • A string is clamped at both ends and plucked so creates a standing wave. Define upward motion to be positive velocities. When the string is in position c, the instantaneous velocity of points along the string • 1. is zero everywhere • 2. is positive everywhere • 3. is negative everywhere • 4. depends on location c
Harmonic frequencies Standing sound wave in a tube closed at one end: there is a node in pressure at the open end, and an anti-node at the closed end.
Beat frequency • The beat frequency is the difference of the frequencies of the two waves that are being added: