1 13 Outline vibrations, waves, resonance Homework: 1, 2, 15, 30, 41, 45, 51, 64, 67, 101.

2 vibrations Examples: vibrating reed, mass on spring, drum, piano wire, string,… most vibrations are sinusoidal in time, and called “simple harmonic” motions (shm)

3 terminology x: displacement A: maximum displacement f: frequency (cycles/s) angular frequency  : (rad/s) k: spring constant (N/m)

4 sinusoidal nature of vibrations

5 Kinematics of SHM position: frequency: angular frequency: maximums:

6 Dynamics of SHM F = -kx, a = -kx/m E = ½kx 2 + ½mv 2. Ex: k = 10N/m, m = 200grams, A = 10cm.

7 Waves traveling disturbance Transverse Longitudinal

8 wave phenomena interference of waves Examples, noise cancellation headphones, standing waves reflection, refraction, and diffraction.

9 Periodic Waves continuous, well defined amplitude (A), frequency (f), wavelength ( ), and speed v = f. Example: f = 10 hertz, = 3 m. v = (10/s)(3m) = 30m/s.

10 Waves on Strings Wave Velocity depends on: tension in string (F) and, the mass per unit length of string. Example: F=36N, m/L=0.010kg/m

11 Standing Waves Nodes (places with zero amplitude) Anti-nodes (places with maximum amplitude) …waves in which the amplitude at a given location does not vary with time. Due to wave interference. Features:

12 Standing Wave: Both Ends Fixed

13 Standing Wave: One End Fixed, One End Free

14 summary many vibrations are simple harmonic one equation set describes all shm wave speed equations interference of waves & standing waves reflection, refraction, diffraction.

15 Main Results

16 Nature of Sound Waves Longitudinal Oscillations are: Condensations (higher pressure areas) and Rarefactions (lower pressure areas) Sound travels at about 343m/s at room temperature and normal atmospheric pressure

17 Doppler Effect Frequency received is different than the Source frequency due to: Source Motion, Receiver Motion or, a combination of Source and Receiver motions.

18 Example of wavelength distortion due to source motion:

19 values of “A” and “f”?

20 Decibels intensity level where I o = 1.0x W/m 2. Example: Intensity of sound is 4.0x10 -5 W/m 2. Intensity level is

21 Sound Intensity (I) Intensity = power/area = P/A [watt/meter 2 ] Spherical Radiation I = P/4  r 2. Example: Small speaker emits 1.0W of sound in all directions. Intensity 10m from the speaker is 1.0/(4  10 2 ) W/m 2.

22 Frequency of Sound Audible Range: 20Hz to 20,000Hz Infrasonic: f < 20Hz Ultrasonic: f > 20,000Hz

23 sinusoidal nature of shm position of blue mass moving on spring turns out to be same as the horizontal position of an object in uniform circular motion.

24 small angles Simple Pendulum