LNK2LRN™ 2016/17 IB Physics Oscillations and Waves.

1. Much of what we need to know about waves can be found by observing

water waves. In doing so, we find two major features of all waves:

(a) a wave is a traveling disturbance, and (b) a wave carries energy from

place to place.

2. Wave motion also has properties of SHM since wave particles vibrate

around an equilibrium position as the wave travels.

3. There are three kinds of waves: transverse, longitudinal, and surface

waves. These are based on the movement of wave particles relative to the

wave velocity.

4. For a transverse wave, vibrations are perpendicular to wave velocity. In a

longitudinal wave, vibrations are parallel to wave velocity. For the third kind,

surface waves (also called water waves), particles move both perpendicular

and parallel to the direction of the wave's motion.

5. Transverse and longitudinal waves are also called periodic waves because

they consist of cycles or patterns that are produced over and over again by

the source.

6. The terms that the study of waves share with SHM are cycle, amplitude,

period, and frequency.

7. Mechanical waves, such as sound waves or waves on a rope, for example

require a medium. Electromagnetic waves, such as light and radio waves, do

not need a medium.

8. Waves transfer energy, either by mechanical or electromagnetic means,

without the transfer of matter.

9. The shortest distance between points where the wave pattern starts to

repeat itself is called the wavelength, and is indicated by the Greek letter,

lambda, λ.

10. A wave disturbance moves in straight lines in all directions away from the

source (rectilinear propagation). This allows us to use the distance-rate-time

equation d = v·t .

11. The frequency ( in sec.^-1 or Hertz, Hz.) of a wave, given by f, is the

number of vibrations per second of any one point on a wave.

12. Period, the reciprocal of frequency, T = 1/f , is the time for a wave to

pass by.

13. The velocity of a wave, the distance a point on a wave moves in a unit

time interval can be calculated using the wave equation, v = f·λ.

14. The amplitude of a wave is the maximum displacement from the

equilibrium position.

15. The highest point above the equilibrium position is called the crest, and

the lowest point below is called the trough.

16. Energy transferred by a wave is proportional to the square of the

amplitude.

17. The speed of a wave depends on the properties of the medium through

which it travels. Research dealing with waves carried by a string produced

the equation v = √(F/µ), where F is the tension in the string, and µ is the

mass per unit length, µ = m/L.

18. If two or more waves are moving through a medium, the resultant wave

is found by adding amplitudes together, point by point. This is known as the

Principle of Superposition.

19. Standing waves are formed when two waves having the same frequency,

amplitude and wavelength, travel in opposite directions in a medium and

interfere.

20. When waves reach a boundary between two media, they are partially

transmitted and reflected. The amount of reflection depends on how much

the two media differ.

21. When a wave moves from a more dense to a less dense medium, the

reflected wave is erect. But in moving from less dense to more dense, the

reflected wave is inverted.

22. Maximum destructive interference produces nodes while maximum

constructive interference produces antinodes.

23. Waves are reflected from a barrier at the same angle, measured against

the normal, as they approach it.

24. The Law of Reflection states that the angle of incidence equals the

angle of reflection, m ⁄ (i) = m ⁄ (r) .

25. The spreading of waves around the edge of a barrier is known as

diffraction. While the change in direction of waves at the boundary of

two different media is known as refraction.

26. Sound, produced by vibrating objects, is a longitudinal wave

transmitted through a gas, liquid, or solid. For sound, instead of crest

and trough, we use the terms condensation and rarefaction.

27. A sound wave is an oscillation in the pressure of the medium, with

the ear and brain perceiving the amplitude as loudness or intensity, or

I = P/(4πr²).

28. The frequency of a sound wave determines its pitch, and on the

musical scale, two notes that differ by one octave have pitches in ratio

2:1. A sound wave of a single frequency is called a pure tone.

29. For most humans, the sonic spectrum consists of frequencies between

20 Hz and 20 kHz. Infrasound is <20 Hz., while ultrasound is >20 kHz.

30. The Doppler shift is the change in frequency of a sound caused by motion

 of either the source, s, or observer, o. The apparent frequency can be

calculated using the equation, f_o = f_s·((v +/– v_o)/(v –/+ v_s)).

31. The amplitude of a sound wave is measured on a scale of decibels (dB),

with β=(10 dB)·log(I/I_o). The threshold of hearing is, I_o = 1.0x10^-12W/m².

32. The speed of sound in air at 0.0^oC is 331.5 m/s, and increases by .60 m/s

per degree rise in air temperature. Speed depends on medium.

33. In an Ideal Gas the speed of sound is given by v =√(γkT/m), where

γ = c_p/c_v, k is Boltzmann's constant, T is the Kelvin temperature, and m is

the mass of a molecule of the gas.

34. In a liquid v =√(B_ad/ρ), where B_ad is the adiabatic bulk modulus, and

ρ is the mass density. For a solid (long slender bar) we have, v =√(Υ/ρ),

where Υ, the Greek letter upsilon, is Young's modulus.

37. Most sounds consist of waves with more than one frequency with the

quality of the wave called timbre.

and still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.

View Wave Slides.    View Superposition Slides. 

Problem Set #1 on Waves. Click HERE.

Problem Set #2 on Waves. Click HERE.

For the Speed of Sound Lab Handout. Click HERE.

For the Lab Abstract template. Click HERE.