Process
1.Describe and define SHM.
- What is simple harmonic motion?
- Circular SHM
- SHM in a Sinusodial Graph
- SHM Animation
- Condition: As an object leaves equilibrium, Hooke’s law states that the force needed to bring it back to equilibrium is directly proportional to the distance
2. Relate energy and speed to simple harmonic motion.
- When looking at a sinusoidal graph of SHM, as the mass goes down and touches the bottom, the velocity is 0; the same applies when the mass reaches the top.
- Through the animation, you see that velocity is changing; therefore, there is acceleration.
- Essentially, Simple Harmonic Motion is a fluctuation between Potential and Kinetic Energy. Potential energy equals 0 when it reaches the equilibrium point. This makes sense, as the equation for Potential energy in a spring is PE=1/2kx squared
- http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html
- http://www.phy.hk/wiki/englishhtm/SpringSHM.htm
3. Describe how force, velocity, and acceleration of a vibration object change.
- Force in SHM deals directly with Hooke’s law with the equation F=-kx, where F is the force, -k is the spring constant, and x is the displacement.
§ Not all apply to this; those that do are called elastic
§ What is the spring constant of a spring that stretches 12 cm when an object weighing 24 N is hung from it?
o If the vibrating object is in SHM, its acceleration is directly proportional to its displacement
o Velocity is always changing; as it approaches an extreme, velocity decreases; as it approaches equilibrium, velocity increases
4. Identify the amplitude of a wave and relate it to energy.
- Go to this website to manipulate the amplitude
- Based on the changes, what is the amplitude a measure of? Does it vary when differentiating between distance from the crest and distance from the trough?
- Amplitude Concepts
- Are energy and amplitude directly or indirectly proportionate? Go here to find out
5/6. Define and relate period and frequency and calculate period/frequency.
- Period is defined as the duration of one sinusoidal cycle; Frequency is the number of cycles in a given time (measured in Hz, or reciprocal seconds)
- They are both reciprocals of each other; T(for period)=1/f and f=1/T
- Frequency Concepts
§ If the Frequency of a traverse wave is 20 Hz, what is the period?
§ If the period of a longitudinal wave is 5 s, what is the Frequency?
7. Describe the motion of a pendulum
· Question: does a pendulum exhibit Simple Harmonic Motion? If so, in what ways?
· http://www.myphysicslab.com/pendulum1.html
· Vary the mass/length of the pendulum. What effects do these have on Frequency? What about amplitude? Why is this?
· The equation for a pendulum is T=2π times the square root of length/gravity.
o On a planet with an unknown value of g, the period of a 75 cm pendulum is 1.8 s. Solve for g.
· Pendulums have two forces that act upon them: Tension and Gravity. When at the left or right extremes, adding both of these forces together shows the net force is in the opposite direction; this accounts for the back and forth movement of pendulums.
***New Topic***
Simple Pendulums and Physical Pendulums
Simple Pendlums differ from Physical Pendlums in the fact that the mass attached to Simple Pendulums is either ignored or is negligible. When there is a larger mass attached, this changes things a bit.
The equation for acceleration applies to torque in Physical pendulum, where τ=Iα or Torque=Moment of Inertia times Angluar Acceleration. So, by looking at the equation for torque, τ=F(gravity) x (R sinθ) , one can apply this equation for Torque in pendulum masses:
τ= (-9.8m/s² x Mass) x Lcm x sin θ
and I=mr²
When Lcm is the distance from the top of the mass to its center of mass.
So, using these values, we can find the period of a physical pendulum
T=2π x (I/τ)
8. Distinguish local particle vibrations from overall wave motion.
- During wave motion, it displaces local air particles that allow these waves to be transmitted (sound waves is an example). While these particles move like a wave (displaced from equilibrium), they are not waves. It is the actual wave itself that is being passed through air particle vibration.
9. Differentiate between pulse waves and periodic waves.
- We have already covered periodic waves (hint: they are a part of SHM). Go to this website.
- How do pulse waves appear to be different? If you still don’t understand, go here.
10. Differentiate between longitudinal and transverse waves.
- Longitudinal waves move parallel to the source of displacement. These include sound waves.
- Transverse waves move perpendicular to the source of displacement.
- Transverse and Longitudinal Waves Animation
11. Solve problems involving wave frequency, speed, and wavelength.
- Previous equations have already been given relating Frequency and period. However, there is another equation. λ=velocity (m/s)/frequency (Hz)
- What is the velocity of a periodic wave that has a frequency of 3.50 Hz and a wavelength of 0.700 m?
- The speed of a transverse wave in a string is 15.0 m/s. If the frequency is 6 kHz, what is the wavelength?
12-13, 15. Apply and define superposition principle, differentiate between constructive and destructive interference, identify nodes and antinodes
· The principle of superposition states that the displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves.
· When two or more waves collide, it is called interference.
· When two waves that have a crest colliding with a crest or a trough with a trough collide, the result is a greater wave with the sum of the amplitudes. The point at which amplitude is the highest is called the antinode. This kind of interference where the amplitude is greater is known as constructive interference.
Constructive Interference Animation
· When a wave crest and a wave trough collide, destructive interference occurs. When they have the same amplitudes but in opposite directions, when they collide, the wave is essentially “flattened out”. The node is the center part that stays stationary.
· When a crest and a trough collide and one of them has a larger amplitude, the superpositioned wave is the algebraic sum of the two (troughs have a negative amplitude)`
14. Define standing wave
- By definition, a standing wave is a wave that seems to be standing still as a result of the interference of two waves moving in opposite directions.
- It seems like the wave is not stopping. The places in which the displacement remains the same are called the nodes. The places with changing displacements are called anti-nodes. Go to this website. see what these look like.
16. Define resonance.
- Resonance occurs when small forces are applied at regular intervals to a vibrating or oscillating object. Resonance Animation
- Resonance is also a major part of sound. However, to produce a certain sound, both the vibrating object and the substance on which is resonates have to have specific qualities.
- Think of a child’s swing; with each push at a certain place, the height (amplitude) increases; what would happen if you tried to double the frequency at that place? Would it work? What does this illustrate about finding the resonance of objects?
17. Explain how sound waves are produced.
- Sound waves are created when tense strings vibrate/oscillate. Sound waves are longitudinal (one of the few) and must travel through matter. Why is it ironic, then, that there are sounds in movies that take place in outer space battles?
- Refer back to the Longitudinal Animation to get an idea of how they move. Rather than pushing air particle up and down, they shift side to side in the direction of the wave.
18. Relate Frequency to Pitch.
- The higher the pitch, the higher the frequency.
- Applying your past knowledge of waves, would a shorter wavelength or a longer wavelength create a higher frequency?
- http://cnx.org/content/m11060/latest/
- Frequency and Pitch Lab
- Does volume play a role in pitch? If not, what does it change in sound waves?
19. Compare speed of sound in various media.
- Sound waves depend particles through which they can pass. Which state of matter can you infer has the highest speed of sound?
- The equation for the speed of sound in dry air is 331.4 + 0.6T, where T is temperature Centigrade.
§ What is the speed of sound in a room that is 28.4 degrees Centigrade?
§ Which do you infer to have the highest speed of sound? Were you right or wrong? Why do solids have a higher speed of sound?
21. Explain the Doppler Effect
- The Doppler Effect is a phenomena when there is a change in frequency of sound caused by the movement of either the source, the detector, or both. What could be some examples of this?
- Go here. Doppler Effect Animation
- How does the particle’s displacement vary when the velocity is less than one? How about when it passes “Mach One”? What is this called (Hint: The first word is also the name of a blue-haired hedgehog, and no, I’m not talking about Alex Martin)?
***New Topic***
While it is determined that the farther away one is from a source, the frequency is directly proportionate. However, one can find the specific frequency rather than using such vague terms.
The equation Fd = Fs (v-vd
v-vs )
Where the Frequency perceived by the detector equals the Frequency of a wave multiplied by the quantity of the velocity of the sound wave minus the velocity of the detector divided by the velocity of the sound wave minus the speed of the sound’s source.
Practice Problems
· You are traveling in a car travelling at 25.0 m/s towards a siren on a pole. If the siren’s frequency is 265 Hz, what frequency do you hear? Use 343 m/s as the speed of sound.
· A submarine is moving towards another submarine at 9.20 m/s. It emits a 3.50 MHz ultrasound. What frequency would the second submarine, moving at 6 m/s, detect? The speed of sound in water is 1482 m/s.
20. Relate plane waves to spherical waves.
· A plane wave is a constant frequency wave whose wave fronts are infinite parallel planes of constant amplitude.
· This seems a bit confusing, but this picture makes it a bit more clear.
· A spherical wave is where a wave is formed in which waves travel outward from the center. A good example would be a ripple in a pond.
· Both are three dimensional. In making relation to transversal and longitudinal waves, which of the two do plane waves relate to? What about spherical waves?
22-23. Calculate the intensity of sound waves and relate intensity, decibel level, and perceived loudness.
- When we did the resonance virtual lab, we saw that volume varied with the amplitude of sound waves.
- To determine sound intensity, the equation I=P/Area
- When I is intensity, P is power in Watts, and Area is in meters squares.
- This is measured in W/m². To calculate in decibels use the equation
- I(dB)=10log10 x I/It
- Where I(dB) is intensity in decibels, I is intensity in W/m squared and It is the threshold of hearing, which equals 10 to the -12 power W/m²
- What is the decibel level of a sound that is 7.8 to the 14 W/m²?
- This does not determine perceived loudness; this is a factor of hearing capacity, distance from the source, and its frequency.
24. Relate the Doppler Effect to the Big Bang
o Much like the Doppler Effect applies to sound waves, it also applies to light waves as well.
o Go to The Doppler Effect and The Big Bang-Article 1
o What does the shifting of stars to the red side of the EM Spectrum tell us?
o Go to this site The Doppler Effect and The Big Band-Article 2
§ How can scientists determing that the stars are “moving away” from us? What else can this tell us about the universe and how it was made? What is still left unexplained?
