READING QUIZ Two waves can be combined to produce no wave. True False

Physics Help Center NEXT EXAM Wednesday April 7th @7pm to 9pm Room 237 Physics Building: 8am to 5:30pm Ask for help from graduate students on homework and exams Can enter solutions on the computers in the room to check your solution. NEXT EXAM Wednesday April 7th @7pm to 9pm Chapters 10,11,12,13,14,15

WAVES Typically, energy is transported by waves (not matter). Motions can be longitudinal or transverse to the wave transport direction (parallel or perpendicular). Periodic waves can be characterized by: wave length l frequency f period T = 1/f velocity v = lf

In a longitudinal pulse, the disturbance is parallel to the direction of travel. In a transverse pulse, the disturbance is perpendicular to the direction of travel.

Variations in air pressure (and density) move through the air in a sound wave. The graph shows pressure plotted against position. Note: the velocity of sound depends on the medium. It is faster in water than in air, and faster yet in steel.

At any instant a transverse pulse moves along a stretched rope, the shape of the rope can be thought of as a graph of the vertical displacement of the rope plotted against horizontal position.

A harmonic wave results when the end of the rope is moved up and down in simple harmonic motion.

velocity F = tension (force), = mass/length As the raised portion of a pulse approaches a given point on the rope, the tension in the rope acquires an upward component. This causes the next segment to accelerate upward. F = tension (force), = mass/length velocity

Identical waves, traveling on two identical ropes that are spliced together, combine to produce a larger wave.

Two waves, exactly out of phase in their up and down motions, combine to produce no net disturbance on the rope beyond the splice.

Wave addition: Consider two “particles”, baseballs for example. If first one ball is put into a box, and then another ball, there must be two balls in the box. Now consider adding two identical waves on a single string. If the two waves arrive in phase, then the resultant wave motion is twice as big. If the two waves arrive out of phase, then the resultant wave motion is ZERO. With waves, 1 + 1 = 0 is a possibility! (INTERFERENCE)

Two waves of the same amplitude and wavelength are shown traveling in opposite directions on a string. When added A node results at point A and an antinode at point B.

The pattern produced by two waves traveling in opposite directions is called a standing wave. The nodes and antinodes do not move. The distance between adjacent nodes or antinodes is half the wavelength of the original waves.

The first three harmonics are the three simplest standing-wave patterns that can be generated on a guitar string fixed at both ends.

Figure 15.19 The standing wave patterns for the first three harmonics are shown for a tube open at one end and closed at the other. The curves represent the amplitude of back- and-forth molecular motion at each point in the tube.

Consider a guitar string which is one meter long, and produces a note at 440 Hz when plucked from the center. Where should the string be held to produce a note with frequency of 660 Hz?