Topic 4 and 11: SL and HL Waves 

Traveling Waves

1. Describe a wave pulse and a continuous traveling wave.

2. Understand that there is no net motion of the medium through which the wave travels.

3. State that waves transfer energy.

4. Describe and give examples of transverse and longitudinal waves.

• sound is a longitudinal wave

• light is a transverse wave.

6. Describe waves in two dimensions, including the concepts of wave fronts and rays.

    

Wave characteristics

7. Define displacement, amplitude, period, frequency, wavelength and wave speed.

8. Describe the terms crest, trough, compression and rarefaction.

9. Draw and explain displacement–time and displacement–position graphs for transverse and longitudinal waves.

10. Derive and apply the relationship between wave speed, wavelength and frequency.

 v = l f

 

 

Wave Properties 

Reflection, refraction and transmission of waves

11. Sketch incident, reflected and transmitted waves, and the cases of reflection at free and fixed ends.

12. Describe the reflection and transmission of one-dimensional waves at a boundary between two media.

13. State Huygens’ (Pronunciation: 'hI-g&nz) principle.

Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of the wave. The new wave-front is the tangential surface to all of these secondary wavelets.

14. Apply Huygens’ principle to two-dimensional plane waves to show that the angle of incidence is equal to the angle of reflection.
15. Explain refraction using Huygens’ principle.

16. Define refractive index or index of refraction.

n = (speed of light in a vacuum) / (speed of light in the media)

17. Derive Snell’s law for refraction using Huygens’ principle.

18. State and apply Snell’s law.

n₁ sin( θ₁) = n₂ sin(θ₂)

 

Where:

n = index of refraction

   = (speed of light in a vacuum) / (speed of light in the media)

 

θ = incident angle

 

Wave diffraction and interference

19. Explain and discuss qualitatively, using Huygens’ principle, the diffraction of waves by apertures and obstacles.

20. Discuss the effect on diffraction and interference of wavelength compared to obstacle size or aperture size.

21. Describe examples of diffraction.

22. State the principle of superposition and explain what is meant by constructive and destructive interference (only one-dimensional situations).

23. Apply the principle of superposition to find the resultant of two waves.

Doppler effect

20. Describe the Doppler effect for both light and sound.

    f = f₀[ (v + v_r) / (v + v_s) ]

    where:

    v = velocity of wave in the medium (air for sound)

    v_r = velocity of the receiver of the wave

    v_s= velocity of the source of the wave

    f₀= frequency of the wave when v_r= v_s=0

     

    For moving source, wave length changes--shorter when moving toward, longer when moving away

    For moving receiver, velocity changes--faster when moving toward, longer when moving away

Standing Waves

21. Describe the nature of standing waves. 

22. Explain the formation of standing waves in one dimension.

23. Compare standing waves and traveling waves.

     

Boundary conditions and resonance (Core)

24. Explain the concept of resonance and state the conditions necessary for resonance to occur.
    • Energy is continuously added to an object in sync with one of its natural frequency and at a rate that is faster than the vibrational energy is converted into heat.
    • The amplitude of the object's vibration increases until the object breaks or begins emitting energy.

24. Define the term damping and state how it affects resonance. Damping is the process of doing work so that a vibration's mechanical energy is converted into heat. If the damping is high enough, an object will not resonate. The damping force that does work acts in the opposite direction of velocity.
25. Give examples of resonant systems.

    mechanical

    • swing--for large angles, the resonant frequency changes, hence limiting the amplitude
    • pendulum--for large angles, the resonant frequency changes, hence limiting the amplitude
    • spring and mass
    • pipe organ
    • bells

    electrical

    • antennae
    • LC circuit

26. Explain a simple way to evaluate an object's resonant frequency. Hit it with a hammer or in other words, give it a pulse of energy.
27. Note that fundamental frequency and first harmonic are interchangeable terms. An object's natural frequencies are the same thing as its harmonics.
28. Solve problems involving the fundamental and higher harmonic modes.

• stretched strings

• open pipes

• closed pipes