Chapter 14 Vibrations and Waves

Periodic Motion Motion which repeat in a regular cycle Simple Harmonic Motion Occurs if the restoring force is proportional to the displacement from equillibrium Has two quantities 1. Period(T)- time to complete one cycle 2. Amplitude-maximum displacement

Hooke’s Law The force exerted by a spring is equal to the spring constant times the distance the spring is compressed or stretched from its equilibrium position. F= -kx K is the spring constant X is the distance that the spring is stretched from its equilibrium position

Potential Energy in a Spring Pe sp = ½ kx 2 A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end. Determine the spring constant How much PE is stored in the spring when it is stretched this far?

Resonance Occurs when small forces are applied at regular intervals to a vibrating or oscillating object and the amplitude of the vibration increases. Is a special form of simple harmonic motion in which the additions of small amount of force at specific times in the motion of an object cause a larger and larger displacement

Wave Properties What is a wave? A disturbance that carries energy through matter or space of-physics-the-nature-of-waves-video.htm of-physics-the-nature-of-waves-video.htm How are waves classified? Mechanical waves- require a medium Non-mechancial waves- no medium needed Transverse waves- vibrates perpendicular to the direction of the wave’s motion Longitudinal waves- disturbance is in the same direction as or parallel to the direction of the wave’s motion

Comparing waves Wave Type MechanicalNon- mechanical Long. Trans. Sound X X Water X X string X X E/m radiati on X X

Measuring a Wave 1. Velocity(v)  d/t; m/s 2. Amplitude(A)  distance; m 3. Wavelength  distance; m - shortest distance between points where the wave pattern repeats - represented by the greek letter lambda( ) -Crest- high point -Trough- low point = v/f 0l2a.cfm

continued 4. Period(T) – time; s T=1/f 5. Frequency(f)- waves/s  Hz(hertz) f= 1/T

Wave Problem A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4 m, in.271 s. a. What is the speed of the wave? b. What is the wavelength of the wave? c. What is the period of the wave? d. If the frequency was changed to 442 Hz, what would be the new wavelength and period?

Wave Behavior 1. Waves at Boundaries Incident Wave  the wave that strikes the boundary Reflected Wave  returning wave aves/U10l3a.cfm aves/U10l3a.cfm

Cont. 2. Superposition of Waves Principle of Superposition  the displacement of a medium caused by 2 or more waves is the sum of the displacements of the individual waves Interference  result of the superposition of 2 or more waves a. Constructive interference- waves moving in the same direction creates a wave with greater amplitude b. Destructive interference- waves moving in opposite directions creates a wave with a lesser amplitude.

Interference website /waves/U10L3c.cfm

Cont. Standing Waves  2 waves traveling in opposite directions with the same velocity and wavelength a. Nodes- points of minimum vibration b. Antinodes- points of maximum vibration U10l4a.cfm

Waves in Two Dimensions Wave Front- line that represents the crest of a wave in 2 dimension Ray- line drawn at right angle to the crest Incident wave/ray-wave that strikes the boundary Reflected wave/ray-returning wave Normal- shows the direction of the barrier - perpendicular to the barrier U10L3b.cfm

Law of Reflection Angle of incidence equals the angle of reflection Angle of incidence- angle between the normal and incident ray Angle of reflection- angle between the normal and reflected ray Refraction- change of direction of waves at the boundary between 2 different media