Checkpoint 1 Study Guide

Law of exponents

• 10^a / 10^b = 10^(a-b)

• 10^a x 10^b = 10^(a+b)

• (anything)⁰ = 1

Scientific notation

• Single digit number with decimals x 10^a

• Number of exponent is determined by how many spaces the decimal place is moved to the left (positive) or right (negative)

Relationship between frequency and period

• Reciprocals of each other

• Period (T) = 1/f

• Frequency (f) = 1/T

Key conversions

• 1 min = 60 s

• 1 s = 1000 ms

• 1 kHz = 1000 Hz

Wavelength

• λ (lambda) = v or c (speed) / f (frequency)

• Higher frequency → shorter period and wavelength

Sound wave properties

• Compression = high density (packed particles)

• Rarefaction = low density (spaced particles)

Waveform graph vs spectrum graph

• Waveform - x-axis = time, y-axis = displacement or amplitude

• Spectrum - x-axis = frequency, y-axis = amplitude

Relationship between elasticity and inertia

• Elasticity - restoring force that allows recovery from distortion caused by a force

• Inertia - the tendency of a body in motion to remain in motion, and a body at rest to remain at rest unless an external force is applied (Newtons 1st Law of Motion)

• Hooke’s Law - the father you stretch or compress an object, the stronger the force pulling it back toward equilibrium

  • Sound wave → amplitude of vibration is proportional to the magnitude of the force being applied

What is sine?

Sine of an angle = opposite/hypotenuse or y/radius

Sound wave

• Sound is a form of movement or vibration

• Movement or vibration involves change in some quantity overtime

• Sounds can be plotted as a change in some quantity overtime (waveform)

Spectrum

Diagrams one point in time or an averaged period of time

Pure tone

• Single frequency sound which loses amplitude overtime

• One sinusoidal wave

• Example - sound produced by tuning fork

• Dimensions - frequency, amplitude, phase, period, wavelength

  • Only frequency, amplitude and phase determine shape of sinusoidal wave

Parts of a soundwave

Birth of sound

• Source + medium = sound

• Source vibrates and these vibrations are transmitted through a medium

• Both the source and medium have…

  • Mass - amount of matter

  • Elasticity - restoring force that allows recovery from distortion caused by a force

How do sounds travel great distances?

• Sound travels as a wave of energy

• Each air molecule vibrates and transfers its energy to neighboring molecules

• Creates compressions and rarefactions

Physical properties of sound

• Amplitude - amplitude of displacement is proportional to the magnitude of the force applied

• Frequency - number of complete cycles in 1 second (cycle/sec = Hz)

• Period - time it takes to complete one cycle (sec/cycle = T)

• Wavelength - physical distance traveled by the wave during one period

  • Can be measured be measured as the distance between two consecutive compressions, refractions, crests, or troughs

Simple harmonic motion (SMH)

• Motion - something is moving

• Harmonic - movement is regular and repetitive

• Simple - the farther it goes from equilibrium, the stronger the force pulling back

• Examples - tuning fork’s vibrating prongs, pendulum, uniform circular motion

How is SMH sinusoidal?

• Quantity varies overtime in a way that can be mathematically described by a sine wave

• 1 circular cycle = 1 wave cycle

One cycle of vibration

• A = equilibrium (0 degrees)

• B = max positive displacement (90 degrees)

• C = equilibrium (180 degrees)

• D = max negative displacement (270 degrees)

• E = equilibrium (360 degrees)

Amplitude

• Height of waveform

• Types

  • Instantaneous amplitude (v(t)) - displacement of the wave at a particular instant

  • Maximum amplitude (A_max) - largest displacement of the wave from equilibrium

  • Peak-to-peak amplitude (V_pp) - total distance from the positive peak to the negative peak

  • Root Mean Square amplitude (A_RMS) - 70.7% of peak amplitude

Root Mean Square amplitude

• A_RMS = 0.707 x A_max

• Units are micropascals

• Calculates average sound level

When is A_max better at describing a sound then A_RMS?

Impulsive sounds (ex. gun shot)

Instantaneous phase

• The angle, in degrees, at a given point in time

• Instantaneous phase = starting phase + (360/T) x t

Starting phase

The angle, in degrees, when the rotation begins

Phase relationships

• In-phase - two waveforms have same frequency and starting phase

• Out-of-phase - two waveforms have same frequency, but different starting phase

Phase

Position, timing, or point of a cycle that a wave has reached as it travels

How fast does sound travel?

343 m/s

Speed equation

Speed = distance/time