PHYSICS WK1- CH 1-4 THE BASICS AND SOUND WAVES
Chapter 1: Basics of Diagnostic Ultrasound, Units, and Graph Relationships
Graphs in diagnostic ultrasound often report information such as velocity of blood. Familiar structure: X-axis and Y-axis.
Types of relationships on graphs:
Unrelated: no association between the two quantities; points are scattered with no pattern (e.g., hair color vs shoe size; temperature vs day of the week). Result: random scatter.
Related or proportional relationship: the two items are associated in some way, but the exact form of the relationship may not be specified.
Directly related: as one quantity increases, the other also increases (positive correlation). Examples from the lecture: age and experience; skill and practice; exam score and studying.
Inversely related: as one quantity increases, the other decreases (negative correlation). Examples: car gas mileage and engine size; grades vs partying time.
Reciprocal relationship: the inverse relationship where the product of the two quantities tends toward a constant (often 1 in a normalized reciprocal pair). The speaker described: if two numbers are in reciprocal relation, their product is 1, e.g., the reciprocal of 20 is rac{1}{20} and multiplying reciprocals yields 1.
Units are essential: "If a number is given without units, the meaning is ambiguous and can lead to uncertainty." Every numerical value must have a unit (e.g., age in days/months/years; length in cm, meters; etc.).
Basic units list (not all physics-heavy terms explained in depth yet): a mix of common and less familiar unit names; these will be elaborated later in the course.
Scientific notation: a shorthand to express very large or very small numbers. Rules mentioned:
Positive exponent: value > 10
Negative exponent: value < 1
Exponent zero: value between 1 and 10
Concept: shift the decimal point by the exponent when converting powers of 10.
Metric prefixes discussed (with ultrasound context): mega, giga, micro, nano, kilo, milli; and some examples of using them in practice (e.g., MHz for ultrasound frequencies).
Prefix pairings (described as complimentary units):
giga ↔ nano (billion vs billionth)
mega ↔ micro
kilo ↔ milli
echo ↔ Scentsy (appears to be a mispronunciation; likely intended as exa ↔ atto or similar; note the speaker labeled them in a conversational way.)
deca ↔ desi (likely deca ↔ deci; the speaker’s pronunciation is informal here)
Quick reference mnemonic for unit hierarchy used in science: “King Henry died by drinking chocolate milk.”
Idea: start at the base unit (meter, liter, gram) and move left (divide) or right (multiply) along prefixes to convert values. The speaker demonstrated the idea using this mnemonic during the megahertz discussion and other conversions.
Key direction rule:
Going left on the prefix ladder = divide by 10 for each step.
Going right on the prefix ladder = multiply by 10 for each step.
Example context provided: converting large to small units and moving across prefixes.
Practice questions from the lecture (quick quiz style): determine whether pairs are inversely related, directly related, or unrelated.
Cholesterol level and longevity: Inverse relationship.
Smoking and likelihood of cardiovascular disease: Direct relationship.
Years employed and days of vacation earned per year: Direct relationship.
IQ and shoe size: Unrelated.
Caloric intake and weight: Direct relationship.
Hours spent exercising and weight: Direct relationship (though the instructor later suggested it could be inverse if cardio reduces weight; the quiz labeled it as direct).
Alcohol intake and sobriety: Inverse relationship.
Reciprocal of 20: rac{1}{20}; multiplying a number by its reciprocal yields 1.
Quick unit-conversion practice from the lecture:
How many milliliters are in 8 liters? Answer: 8 ext{ L} = 8{,}000 ext{ mL} (since 1 ext{ L} = 1000 ext{ mL}).
How many liters are in 80 milliliters? Discussion in class involved choosing the correct option and moving the decimal point; the rule is to shift the decimal three places to the left when converting from mL to L (since 1,000 mL = 1 L), giving 80 ext{ mL} = 0.080 ext{ L}. The mnemonic “King Henry died by drinking chocolate milk” helps remember the three-step prefix order and decimal shifts. Note: the instructor emphasized the left-right direction for division vs multiplication when converting across prefixes.
Frequency example: if you hear about a probe described as 3 MHz, that is 3 ext{ MHz} = 3 imes 10^{6} ext{ Hz} = 3{,}000{,}000 ext{ Hz}. 3 MHz is a common ultrasonic frequency.
Prefix speeds and their usage in ultrasound: when describing probe capabilities, you’ll often see MHz values (megahertz).
Chapter 1 wrap-up and context for Chapter 2: The lecture transitions from basic unit management and relationships to the physics of sound waves and acoustic concepts. The instructor notes that Chapter 1 (the basics) covers units, measurement, and graphs, and that Chapter 2 will delve into sound waves, media, and propagation properties.
Chapter 2: Sound Waves and Acoustic Principles
All waves carry energy from one location to another (examples given: heat waves, sound waves, magnetic and light waves). This is a general wave property.
Sound is a mechanical wave in which particles in the medium move and vibrate from a fixed position.
Sound cannot travel through a vacuum; it must travel through a medium (air, liquid, body tissues, blood, etc.).
A vacuum (empty space) has no medium, so sound cannot propagate there.
Mediums for ultrasound context:
Air, liquids, body tissues (including blood) are examples of media through which ultrasound can travel.
A vacuum is not suitable for sound propagation.
Acoustic propagation properties vs biologic effects:
Acoustic propagation properties: how the medium affects the sound wave (speed, attenuation, reflection, refraction, etc.).
Biologic effects: how the sound wave affects tissue through which it passes (thermal, mechanical effects, cavitation considerations in ultrasound are implied contextually, though not elaborated in the transcript).
Acoustic variables (the three primary descriptors of a sound wave):
Pressure (p): concentration of force per area, measured in pascals, ext{Pa}.
Density (ρ): mass per unit volume, measured in kilograms per cubic meter, rac{ ext{kg}}{ ext{m}^3} (the transcript uses cm^3 in some contexts; the typical ultrasound context uses m^3 for SI units).
Distance (displacement, often denoted by s or x): measure of particle motion, measured in units like centimeters or millimeters, in ultrasound typically millimeters or centimeters.
Key point about acoustic variables:
If one (or more) of pressure, density, or distance oscillates rhythmically, the wave is a sound wave.
If a variable other than these oscillates rhythmically, the wave is not a sound wave.
Acoustic variables are also referred to as acoustic properties or parameters that distinguish sound waves from other wave types.
Acoustic waves are also known as acoustic waves; refer to the same phenomenon described in the table (“c table 2.1 on page 12”).
Clarifying density units and three-dimensionality:
Density is given as mass per volume; units such as ext{kg}/ ext{cm}^3 indicate three-dimensional volume in the denominator (cm^3) to reflect a 3D volume.
When converting density units, remember the linear dimensions are in 3D space; thus, density uses volume units in the denominator.
Student questions and clarifications:
The density unit question: density is in units like ext{kg}/ ext{m}^3 or ext{kg}/ ext{cm}^3; the power of three in the volume unit indicates the 3D nature of a volume element.
If a wave has only one of the three acoustic variables oscillating, is it still a sound wave? Yes, as long as at least one of pressure, density, or displacement/distance oscillates rhythmically.
Seven acoustic parameters used to describe a sound wave (when identified as a sound wave):
Period, Frequency, Amplitude, Power, Intensity, Wavelength, Propagation speed.
These are standard descriptors of a wave’s behavior; the lecture lists them as the seven fundamental acoustic parameters to be described for each sound wave.
Transverse vs longitudinal waves (with a simple illustrative example):
Transverse wave: particles move perpendicular (at a right angle) to the direction of wave propagation. Example: holding a string and moving it up and down creates a transverse wave; the energy travels horizontally while the string moves vertically.
Longitudinal wave: particles move parallel to the direction of wave propagation. Sound waves in air and tissues are primarily longitudinal.
Summary of ultrasound-specific context for Chapter 2:
Ultrasound uses mechanical waves that require a medium; body tissues serve as the medium for diagnostic ultrasound in clinical use.
The speed, attenuation, and interaction of ultrasound with tissues depend on the medium’s acoustic properties (pressure, density, distance fluctuations), which in turn shape how images are formed and interpreted.
Practical takeaways and connections:
Understanding that sound waves propagate only in media helps explain why ultrasound is patient-specific and tissue-dependent.
The seven acoustic parameters provide a framework for analyzing any given ultrasound signal: you can measure or infer period, frequency, amplitude, power, intensity, wavelength, and speed to characterize the wave.
The King Henry mnemonic, prefixes, and unit conversions introduced in Chapter 1 are foundational for working with ultrasound frequencies (MHz) and interpreting device specifications (e.g., probe frequency in MHz).
Key formulas and concepts (LaTeX)
Reciprocal relation (product equals 1): a imes rac{1}{a} = 1. Inverse/pair examples discussed: the reciprocal of 20 is rac{1}{20}, and multiplying a number by its reciprocal yields 1.
Frequency and time relationship (conceptual): f = rac{1}{T} where T is the period of the wave.
Frequency unit conversion: 1 ext{ MHz} = 10^{6} ext{ Hz}; thus, 3 ext{ MHz} = 3 imes 10^{6} ext{ Hz} = 3{,}000{,}000 ext{ Hz}.
Length/volume unit conversions (examples):
1 ext{ L} = 1000 ext{ mL}, so 8 ext{ L} = 8000 ext{ mL}.
80 ext{ mL} = 0.080 ext{ L}.
Density unit clarification: density is mass per unit volume; SI unit is rac{ ext{kg}}{ ext{m}^3}; in some contexts, density might be expressed as rac{ ext{kg}}{ ext{cm}^3}, where cm^3 reflects a cubic centimeter volume in three dimensions.
Acoustic variables (summary):
Pressure: p, measured in ext{Pa} (pascals).
Density:
ho, measured in rac{ ext{kg}}{ ext{m}^3} or rac{ ext{kg}}{ ext{cm}^3}.Distance (displacement): measured in units like ext{m}, ext{cm}, or ext{mm}.
Seven acoustic parameters (names): T, f, A, P, I, \lambda, c where
T = period,
f = frequency,
A = amplitude,
P = power,
I = intensity,
\lambda = wavelength,
c = propagation speed.
Quick real-world and study-context notes
Chapter 1 vs Chapter 2 alignment: the lecturer notes that Chapter 1 (the basics) covers units, graphs, and relationships, while Chapter 2 dives into sound waves, media interaction, and propagation—core physics for ultrasound imaging.
Real-world relevance: understanding units, prefix hierarchies, and reciprocal relationships improves accuracy in reporting measurements, device setup, and data interpretation in ultrasound practice.
Ethical and practical implications (implicit):
Accurate units and conversions are essential for patient safety (dosage, exposure times) and diagnostic accuracy.
Understanding how waves interact with tissue informs safe ultrasound use and interpretation of images.
Note on classroom context: The transcript reflects a live classroom session with some student questions and potential inconsistencies in how prefixes were named. The core ideas, definitions, and conversions highlighted here reflect the material as presented and are aligned with standard ultrasound concepts where applicable. If a specific prefix naming was mispronounced, rely on standard prefixes (e.g., kilo, mega, giga, nano, micro, milli) and their relationships to base units for exam purposes.