Simple Harmonic Motion Waves Vocabulary Period the time
Simple Harmonic Motion & Waves
Vocabulary • Period: the time for one cycle of simple harmonic motion, or the time for a full wavelength to pass a position. • Frequency: the number of cycles, or the number of wavelengths passing a position, in one second. – The unit for frequency is Hertz which means per second.
Vocabulary Contd. • Amplitude: the distance from the midpoint of a wave to its crest or trough or the distance from the midpoint of simple harmonic motion to the maximum displacement • Wavelength: measured from peak to peak or between any successive identical points on a wave.
Vocabulary Contd. • Spring Constant: k, measured in units of newtons per meter (N/m), is related to the stiffness of the spring • Restoring force: is any force that always pushes an object toward an equilibrium position.
Vocabulary Contd. • Nodes: are the stationary points on a standing wave. • Antinodes: are the positions on standing waves with the largest amplitudes.
Simple Harmonic Motion (SHM) • Refers to the back-and-forth oscillation whose position-time graph looks like a sine function • Examples: mass vibrating on a spring and a pendulum
Period of a mass on a spring in SHM Note: The AP exam probably ask something along the lines of if you double the mass what affect does that have on the period
What about Amplitude? • What happens to the period if you double the amplitude?
Frequency vs. Period • Frequency and period are inverses of one another
Restoring Force • The amount of restoring force exerted by a spring is given as Hooke’s Law
Restoring Force • The force of the spring is greatest when the spring is most stretched, but zero at the equilibrium positon. • Acceleration changes (max at the endpoints to zero in the middle), you cannot use kinematics for a spring (kinematics is used for constant acceleration ONLY) • SO when looking for the speed, you must use the conservation of energy
Potential Energy of a Spring • Spring potential energy
Energy • The energy stored in the spring is largest at the endpoints and zero at the equilibrium position. • Spring energy is completely converted into kinetic energy at equilibrium. • So where is the cart’s speed the greatest?
Pendulum • Pendulum can be treated the same as a spring. It’s still in harmonic motion and requires an energy approach not kinematics to determine speed at any position.
Period of a Pendulum • The period of a pendulum Note: Again, the AP exam will probably ask something along the lines of asking you to determine the order from greatest to least of a particular variable.
Ranking 1 • Rank the lettered positions from greatest to least by the bob’s gravitational potential energy. Start D A B C
Ranking 2 • Rank the lettered positions from greatest to least by the bob’s total mechanical energy. Start D A B C
Ranking 3 • Rank the lettered positions from greatest to least by the bob’s speed Start D A B C
Challenge Question • The gravitational field at the surface of Jupiter is 26 n/kg and on the surface of the Moon, 1. 6 N/kg. Rank this pendulum’s period near these two planets and earth. • What about the ranking of the frequency?
Mechanical Waves • The AP exam focuses on Mechanical waves like sound or waves on the surface of an ocean, not light waves (electromagnetic)
Transverse Waves • Whenever the motion of a material is at right angles to the direction in which the wave travels, the wave is a transverse wave.
Energy • The energy carried by the wave depends on the wave’s amplitude. • Draw a wave the with low energy and one with high energy.
Frequency • When a wave changes materials, its frequency remains the same. • However, the speed and wavelength may increase.
Longitudinal Waves • When a material vibrates parallel to the direction of the wave, the wave is a longitudinal wave.
Wavelength • Try drawing a longitudinal wave and labeling a wavelength. – A wavelength is defined as the distance between two identical positions on the wave.
Interference • When two waves collide, they don’t bounce or stick like objects do. Rather, the waves interfere. They form one single wave for just a moment, and then the waves continue on their merry way.
Standing Waves • Is a wave that appears to stay in one place.
Standing Waves • Generally, when you pluck a string, you produce a standing wave of the longest possible wavelength and thus the smallest possible frequency.
Wavelength • The wavelength of a standing wave is twice the node-to-node distance.
Frequency • For a string fixed at both ends, or for a pipe open at both ends, the smallest frequency of standing waves is given by
Pitch & Loudness • The loudness of a note depends on the sound wave’s amplitude. • The pitch of a musical note depends on the sound wave’s frequency
Frequency • For a pipe closed at one end, or for a string fixed at one end but free at the other, the smallest frequency of standing waves is given by 4
Beats • Beats are rhythmic interference that occurs when two notes of unequal but close frequencies are played.
Doppler Effect • The Doppler Effect is the apparent change in a wave’s frequency that you observe whenever the source of the wave is moving toward or away from you.