Physics: Math Basics & Sound Waves

Physics: Math Basics

The Math Basics: Order of Operations

  • PEMDAS is a mnemonic for the order of operations:
    • P: Parenthesis
    • E: Exponents
    • M: Multiplication
    • D: Division
    • A: Addition
    • S: Subtraction

Examples and Important Exponents

  • Examples of order of operations:
    • 2 + 5 - 3 = 4
    • 2 + 5 \times 3 = 17
    • (2 + 5) \times 3 = 21
    • (2^2 + 5) \times 3 = (4 + 5) \times 3 = 9 \times 3 = 27
  • Important exponents:
    • 10^2 = 1 \times 10^2 = 100
    • 10^3 = 1 \times 10^3 = 1000
    • 10^{-2} = 1 \times 10^{-2} = 0.01
    • 10^{-3} = 1 \times 10^{-3} = 0.001

Examples: Other Important Exponents

  • Other important exponents:
    • 2^2 = 2 \times 2 = 4
    • 2^3 = 2 \times 2 \times 2 = 8
    • 2^4 = 2 \times 2 \times 2 \times 2 = 16
    • 3^2 = 3 \times 3 = 9
    • 3^3 = 3 \times 3 \times 3 = 27
    • 3^4 = 3 \times 3 \times 3 \times 3 = 81

Relationships Between Terms

  • Unrelated: No relation between terms.
    • Example: Test score is unrelated to the student’s seat number.
  • Directly Related: When one item increases, the other increases.
    • Example: Skill is directly related/directly proportional to practice.
  • Inversely Related: When one item increases, the other decreases.
    • Example: When temperature goes down, sweater sales go up.
  • Reciprocal Relationship: Multiplication of reciprocal numbers equals one.

Units of Measurement

  • All numerical values must have a corresponding unit.
    • Example: Runner finished 2 miles race in 20 minutes.
  • Conversions:
    • Example: How many minutes are there in one hour?
  • Notes:
    • Unit is very important to consider with the numerical value.
    • Percent is unitless.
    • Increase By a factor: Multiply by that number.
    • Decrease by a factor: Divide by that number.

Metric System - Powers of Ten

  • Exponents, prefix, symbol, meaning:
    • 10^9: giga, G, billion
    • 10^6: mega, M, million
    • 10^3: kilo, k, thousand
    • 10^2: hecto, h, hundred
    • 10^1: deca, da, ten
    • 10^{-1}: deci, d, tenth
    • 10^{-2}: centi, c, hundredth
    • 10^{-3}: milli, m, thousandth
    • 10^{-6}: micro, µ, millionth
    • 10^{-9}: nano, n, billionth

Scientific Notation

  • Scientific Notation: Shorthand representation of very big or very small number:
    • Examples:
      • 1,000 = 10^3
      • 2,000 = 2 \times 1,000 = 2 \times 10^3
      • .001 = 10^{-3}
      • .002 = 2 \times .001 = 2 \times 10^{-3}

Complimentary Units Pairs

  • Prefixes Abbreviations:
    • billions & billionth: giga and nano, G and n
    • millions & millionths: mega and micro, M and µ
    • thousands & thousandths: kilo and milli, k and m
    • hundreds & hundredths: hecto and centi, h and c
    • tens & tenths: deca and deci, da and d

The Graph

  • X-axis (Horizontal axis): runs side to side
  • Y-axis (Vertical axis): runs up and down

Review Questions

  • Are the following pairs inversely related, directly related, or unrelated?
    • Cholesterol level and longevity
    • Smoking and the likelihood of cardiovascular disease
    • Years employed and the days of vacation earned per year
    • IQ and shoe size
    • Calorie intake and weight
    • Hours spent exercising and weight
    • Alcohol intake and sobriety
  • What is reciprocal of 20?

Sound Waves

  • Sound is mechanical wave: The particles move back and fourth.
  • Sound is longitudional wave: The wave travel in straight line.
  • Biologic effect: The effects of sound wave on medium.
  • Acoustic propagation properties: Effects of medium on sound wave
  • Sound cannot travel through vacuum.

Transverse Waves

  • Particles displace perpendicular to the direction of propagation of the wave.
    • Ex: Wave on a string and ripple on a pond

Longitudinal Waves

  • Particles displace parallel to the propagation of the wave
    • Ex: Sound wave in the air and seismic p-wave created during earthquakes and explosions.

In-Phase and Out of Phase Waves

  • In-phase: Peaks at the same time
  • Out of phase: Peaks at different times

Interference

  • Combination of two or more than two waves produce interference.
  • Original waves lose their identity.
  • In-phase waves go through interference called constructive interference (resultant wave is bigger) while out of phase waves undergo destructive interference (resultant wave is smaller).

Different Frequencies

  • With different frequency waves, both constructive and destructive interference occur.

Acoustic Variables

  • The alteration in these four variables generate a sound wave:
    • A) Pressure: Force per unit area
      • Unit: pascals (Pa)
    • B) Density: Mass per unit volume
      • Unit: kg/cm3
    • C) Distance: Measure of length
      • Unit: cm, feet, mile
    • D) Temperature: Degree of hotness or coldness of a body or environment
      • Unit: 0C or 0F
  • Rhythmic movement of any of the four variable generate sound wave (acoustic wave).
    • If there is movement of any other variable then the wave is not a sound wave.

Acoustic Parameters

  • Acoustic parameters are the parameters required to describe any sound wave.
  • Seven Acoustic parameters:
    • 1. Period
    • 2. Frequency
    • 3. Amplitude
    • 4. Power
    • 5. Intensity
    • 6. Wavelength
    • 7. Propagation speed

Review

  • Define sound wave.
  • Define biologic effect.
  • What do waves transfer from one place to another?
  • Name three acoustic variables.
  • Unit of all three variables.
  • Name seven acoustic variables.
  • What in in phase and out of phase waves?
  • When do two waves have constructive and destructive interface?