Lecture 20: Waves

1. Lecture 20:Waves • Definition of a Wave • Longitudinal vs. Transverse Waves • Speed of Waves • Harmonic Waves • Interference and Superposition • Reflection • Standing Waves

2. What is a wave ? • According to our text: • A wave is a disturbance that travels away from its source. • Examples: • Sound waves (air moves back & forth) • Stadium waves (people move up & down) • Water waves (water moves up & down and back & forth) • Light waves

3. Types of Waves • Transverse: The medium oscillates perpendicular to the direction the wave is moving. • Waves on a String • Water (partially) • Longitudinal: The medium oscillates in the same direction as the wave is moving. • Sound • Water (partially)

4. Speed of Waves The speed of a wave is a constant that depends only on the medium, not on amplitude, wavelength or period (similar to SHM).

5. Harmonic Waves y(x,t) = A cos(wt –kx) amplitude = A angular frequency = w = 2f wave number = k = 2p/l

6. Amplitude, Wavelength, and Period Wavelength  A A • Amplitude: The maximum displacement A of a point on the wave. • Wavelength: The distance  between identical points on the wave. • Period: The time T for a point on the wave to undergo one complete oscillation. T = 2/ • Speed: The wave moves one wavelength  in one period T. v = / Tv = f

7. Interference and Superposition • When two waves overlap, the amplitudes add. • Constructive:increases amplitude • Destructive:decreases amplitude

8. Reflection • When a wave travels from one medium to another, reflection occurs at the boundary. • Some of the wave reflects backwards from the boundary. • Reflecting off a fixed boundry:the reflected wave is inverted. • Reflecting off a free boundry :the reflected wave is upright.

9. Standing Waves • Fundamental: n=1 • ln = 2L/n • v = l f

10. L = l / 2 f1= fundamental frequency (lowest possible) v = l fcan be used to find f, v, or l L = l f2= first overtone Standing Waves

11. Summary • Wave Types • Transverse (pulse on string, water) • Longitudinal (sound, slinky) • Harmonic Waves • y(x,t) = A cos(wt –kx) or A sin(wt – kx) • Superposition of Waves • Just add amplitudes • Reflection of Waves • (fast to slow gets inverted) • Standing Waves • ln = 2L/n • v = l f

12. L m Standing Wave Example Using the apparatus shown below, a standing wave pattern is set up. The frequency is fixed at 60 Hz. The hanging mass is 50 g and the mass density of the string is 0.12 g/m. What does the length of the string need to be to set up the 4th harmonic (the 3rd overtone)? • First, we will calculate the velocity of the wave: • Second, we will find the wavelength of the wave: • Third, we will determine the length of the string needed.

13. L m Standing Wave Example Using the apparatus shown below, a standing wave pattern is set up. The frequency is fixed at 60 Hz. The hanging mass is 50 g and the mass density of the string is 0.12 g/m. What does the length of the string need to be to set up the 4th harmonic (the 3rd overtone)? • The velocity of the wave: = 63.9 m/s

14. L m Standing Wave Example Using the apparatus shown below, a standing wave pattern is set up. The frequency is fixed at 60 Hz. The hanging mass is 50 g and the mass density of the string is 0.12 g/m. What does the length of the string need to be to set up the 4th harmonic (the 3rd overtone)? • The wavelength of the wave: = 1.065 m

15. L m Standing Wave Example Using the apparatus shown below, a standing wave pattern is set up. The frequency is fixed at 60 Hz. The hanging mass is 50 g and the mass density of the string is 0.12 g/m. What does the length of the string need to be to set up the 4th harmonic (the 3rd overtone)? • The length of the string: = 2.13 m

16. (A) (B) (C) (D) (E)

17. (A) (B) (C) (D)