SPH3U · Unit 4 test review

Waves and Sound: Test Review

Everything for the Unit 4 test on one page: the key facts from all 5 lessons, the mistakes that cost the most marks, and a practice test that points you back to the lessons you need.

Key facts

Wave Anatomy and the Wave Equation

A wave transfers energy without transferring matter.
Transverse waves vibrate perpendicular to travel (light, string); longitudinal waves vibrate parallel (sound).
Sound is longitudinal and needs a medium — it cannot cross a vacuum.
Amplitude is measured from the rest position to a crest, not trough to crest.
$f = \frac{# cycles}{time} = \frac{1}{T}$ — frequency and period are reciprocals.
$v = f λ$ applies to every wave.
The medium fixes the speed and the source fixes the frequency, so entering a new medium changes the wavelength.
Sound travels fastest in solids, slower in liquids, slowest in gases.

The Speed of Sound, Echoes and Mach Number

$v_{so u n d} = (332 + 0.6 T) m/s$ , with $T$ in degrees Celsius.
Every degree Celsius adds about $0.6 m/s$ ; at $20^{\circ} C$ sound travels $344 m/s$ .
$t_{ec h o} = \frac{2 d}{v}$ — the sound makes a round trip, so the distance travelled is twice the distance to the surface.
Rearranged for distance: $d = \frac{v t _{ec h o}}{2}$ .
$mach # = \frac{v _{o bj ec t}}{v _{so u n d}}$ — a unitless ratio.
Mach less than 1 is subsonic, greater than 1 supersonic, greater than 5 hypersonic.
A sonic boom is produced continuously by a supersonic aircraft, not once at the moment it passes Mach 1.
Doppler: approaching sources sound higher, receding sources sound lower. The emitted frequency never changes.

Reflection, Superposition and Beats

Superposition: where waves overlap, the displacement is the sum of the individual displacements.
A pulse reflecting from a fixed end is inverted; from a free end it is upright.
Constructive interference: waves in phase, displacements add, larger amplitude.
Destructive interference: waves out of phase, displacements cancel, smaller or zero amplitude.
Waves pass through each other unchanged — interference only occurs while they overlap.
$f_{b e a t} = ∣ f_{1} - f_{2} ∣ = \frac{# beats}{time} .$
Zero beats means the frequencies are identical, which is how instruments are tuned.
The absolute value means beats cannot tell you which frequency is higher.

Resonance, Harmonics, Intensity and Hearing

A standing wave has nodes (zero displacement) and antinodes (maximum displacement), with adjacent nodes half a wavelength apart.
Resonance is large-amplitude vibration produced by driving a system at one of its natural frequencies.
Strings and open pipes: $l_{n} = \frac{nλ}{2}$ and $f_{n} = n f_{0}$ — all harmonics.
Closed pipes: $l_{n} = \frac{( 2 n - 1 ) λ}{4}$ and $f_{n} = (2 n - 1) f_{0}$ — odd harmonics only.
A closed pipe sounds one octave lower than an open pipe of the same length.
$\frac{I _{2}}{I _{1}} = \frac{r _{1}^{2}}{r _{2}^{2}}$ and $I \propto \frac{1}{d ^{2}}$ — double the distance, quarter the intensity.
$d B = 10 lo g (\frac{I _{2}}{I _{1}})$ . A tenfold intensity increase is $+ 10 dB$ and sounds about twice as loud.
Hearing damage is permanent, cumulative, and depends on both level and exposure time.

Sound in Technology, Medicine and the Environment

Ultrasound is sound above $20 kHz$ ; medical imaging uses $1$ to $20 MHz$ .
Imaging works by echo timing: $d = \frac{v t _{ec h o}}{2}$ , with $v \approx 1540 m/s$ in soft tissue. The factor of two has not gone away.
The reflectors are the boundaries between tissues, not the organs. Gel excludes the air layer that would otherwise reflect the whole pulse.
Resolution is limited by wavelength and $λ = \frac{v}{f}$ , so higher frequency gives finer detail but is absorbed faster and penetrates less deeply.
An echo is one reflection delayed more than about $0.1 s$ ; reverberation is thousands of early reflections merging into a decaying tail.
Hard surfaces reflect and lengthen reverberation; soft porous surfaces absorb and shorten it. Treatment controls sound inside a room, soundproofing keeps it between rooms.
Ontario workplace noise is capped at $85 dB$ over eight hours, and every $3 dB$ above halves the safe time.
Doubling your distance from a source cuts the intensity to a quarter, about $6 dB$ of protection for free.

Where marks get lost

Measuring amplitude from trough to crest. It is measured from the rest position, so that value is twice the amplitude. (Wave Anatomy and the Wave Equation)
Thinking the medium travels with the wave. Only energy moves; the particles oscillate about fixed positions. (Wave Anatomy and the Wave Equation)
Assuming frequency changes when a wave enters a new medium. The frequency is set by the source — the wavelength changes instead. (Wave Anatomy and the Wave Equation)
Believing sound travels faster in air than in solids. Stiffer media carry sound faster, so steel beats water beats air. (Wave Anatomy and the Wave Equation)
Confusing period with frequency. They are reciprocals, so a large frequency means a small period. (Wave Anatomy and the Wave Equation)
Claiming sound can travel through a vacuum. It is a mechanical wave and needs particles to compress. (Wave Anatomy and the Wave Equation)
Putting kelvin into $v = 332 + 0.6 T$ . The formula takes degrees Celsius, and kelvin gives an absurd $500 m/s$ . (The Speed of Sound, Echoes and Mach Number)
Forgetting the factor of two in echo problems, which doubles every distance. (The Speed of Sound, Echoes and Mach Number)
Halving when you should double. Time to distance divides by two; distance to time multiplies by two. (The Speed of Sound, Echoes and Mach Number)
Using the air-temperature formula for sound in water or steel. It applies only to air. (The Speed of Sound, Echoes and Mach Number)
Giving Mach number a unit. It is a ratio of two speeds, so the units cancel. (The Speed of Sound, Echoes and Mach Number)
Comparing an aircraft's speed with the sea-level speed of sound when it is flying in much colder air high above. (The Speed of Sound, Echoes and Mach Number)
Saying a sonic boom happens once, at the instant of 'breaking' the sound barrier. The cone trails continuously. (The Speed of Sound, Echoes and Mach Number)
Adding amplitudes without signs, so a crest meeting a trough appears to grow instead of cancelling. (Reflection, Superposition and Beats)
Thinking waves destroy each other during destructive interference. They pass through and re-emerge unchanged. (Reflection, Superposition and Beats)
Getting the reflection rule backwards. Fixed ends invert; free ends do not. (Reflection, Superposition and Beats)
Forgetting the absolute value on the beat frequency and reporting a negative answer. (Reflection, Superposition and Beats)
Assuming a beat frequency identifies which note is higher. Both $437$ and $443 Hz$ beat at $3 Hz$ against $440$ . (Reflection, Superposition and Beats)
Dividing the frequencies instead of subtracting them. (Reflection, Superposition and Beats)
Expecting audible beats from two widely separated frequencies. Beyond roughly $10 Hz$ apart you just hear two notes. (Reflection, Superposition and Beats)
Using the open-pipe formula on a closed pipe. Closed pipes fit a quarter wavelength and have odd harmonics only. (Resonance, Harmonics, Intensity and Hearing)
Calling the next harmonic above the fundamental in a closed pipe the 'second'. It is the third — there is no second. (Resonance, Harmonics, Intensity and Hearing)
Inverting the intensity ratio, so moving further away appears to make the sound louder. (Resonance, Harmonics, Intensity and Hearing)
Forgetting to square the distances in the inverse square law. (Resonance, Harmonics, Intensity and Hearing)
Thinking $+ 10 dB$ means ten times louder. It is ten times the intensity, which sounds about twice as loud. (Resonance, Harmonics, Intensity and Hearing)
Treating decibels as a linear unit, so $60 + 60$ appears to give $120 dB$ . (Resonance, Harmonics, Intensity and Hearing)
Assuming a string's wavelength equals its length. The fundamental fits only half a wavelength, so $λ = 2 l$ . (Resonance, Harmonics, Intensity and Hearing)
Dropping the factor of two in an ultrasound depth calculation. The pulse still makes a round trip, so every boundary lands at twice its true depth. (Sound in Technology, Medicine and the Environment)
Leaving the echo time in microseconds. A time of $65 μ s$ is $65 \times 1 0^{- 6} s$ , and ignoring the prefix inflates the answer by a factor of a million. (Sound in Technology, Medicine and the Environment)
Claiming a higher-frequency probe is always better. It resolves finer detail but is absorbed much faster, so it may never reach a deep target at all. (Sound in Technology, Medicine and the Environment)
Saying higher frequency travels faster through tissue. The speed is set by the medium at about $1540 m/s$ ; raising the frequency shortens the wavelength instead. (Sound in Technology, Medicine and the Environment)
Confusing echo with reverberation. An echo is one reflection delayed past about $0.1 s$ ; reverberation is the merged tail of thousands of earlier ones. (Sound in Technology, Medicine and the Environment)
Treating acoustic panels as soundproofing. Absorption shortens the reverberation inside a room; keeping sound out of a room needs mass and sealing instead. (Sound in Technology, Medicine and the Environment)
Assuming a louder public-address system fixes a reverberant gym. It raises the reflections by exactly as much as the speech, so intelligibility does not improve. (Sound in Technology, Medicine and the Environment)

Practice test

25 questions from across the unit. Each one shows the lesson it comes from.

Wave Anatomy and the Wave Equation
1
A wave has frequency $40 Hz$ and wavelength $2.5 m$ . What is its speed, in m/s?
m/s
Wave Anatomy and the Wave Equation
2
In a longitudinal wave, how do the particles of the medium move?
Wave Anatomy and the Wave Equation
3
What does a wave transfer from place to place?
Wave Anatomy and the Wave Equation
4
Which property of a sound wave determines how loud it is?
Wave Anatomy and the Wave Equation
5
Order these media from fastest sound speed to slowest.
1. 1Water
2. 2A vacuum
3. 3Air at $20^{\circ} C$
4. 4Steel
The Speed of Sound, Echoes and Mach Number
6
What is the speed of sound in air at $30^{\circ} C$ , in m/s?
m/s
The Speed of Sound, Echoes and Mach Number
7
An echo returns after $2.0 s$ where sound travels at $340 m/s$ . How far away is the reflecting surface, in metres?
m
The Speed of Sound, Echoes and Mach Number
8
An ambulance siren drops in pitch as it passes you. What has happened to the sound the siren emits?
The Speed of Sound, Echoes and Mach Number
9
In the formula $v = 332 + 0.6 T$ , what unit must the temperature be in?
The Speed of Sound, Echoes and Mach Number
10
Order these air temperatures by the speed of sound they produce, fastest first.
1. 1 $20^{\circ} C$
2. 2 $- 20^{\circ} C$
3. 3 $0^{\circ} C$
4. 4 $35^{\circ} C$
Reflection, Superposition and Beats
11
Two tuning forks of $512 Hz$ and $518 Hz$ sound together. What is the beat frequency, in hertz?
Hz
Reflection, Superposition and Beats
12
A pulse travelling along a string reflects from an end clamped firmly to a wall. What happens?
Reflection, Superposition and Beats
13
What principle states that overlapping waves add their displacements?
Reflection, Superposition and Beats
14
How do noise-cancelling headphones reduce unwanted sound?
Reflection, Superposition and Beats
15
A string is tuned against a $440 Hz$ fork. Order these beat frequencies from most in tune to least.
1. 11 beat per second
2. 29 beats per second
3. 35 beats per second
4. 40 beats per second
Resonance, Harmonics, Intensity and Hearing
16
A string $0.80 m$ long vibrates at its fundamental. What is the wavelength, in metres?
m
Resonance, Harmonics, Intensity and Hearing
17
A string has a fundamental of $150 Hz$ . What is the frequency of its fourth harmonic, in hertz?
Hz
Resonance, Harmonics, Intensity and Hearing
18
By how many decibels does the level rise if the intensity increases by a factor of 1000?
dB
Resonance, Harmonics, Intensity and Hearing
19
An increase of $10 dB$ corresponds to what change in intensity?
Resonance, Harmonics, Intensity and Hearing
20
Order these sounds from quietest to loudest.
1. 1Normal conversation ( $60 dB$ )
2. 2Jet engine close up ( $140 dB$ )
3. 3Power tools ( $100 dB$ )
4. 4Rustling leaves ( $20 dB$ )
Sound in Technology, Medicine and the Environment
21
An ultrasound echo returns $40 μ s$ after the pulse is sent. Sound travels at $1540 m/s$ in tissue. How deep is the boundary, in millimetres?
mm
Sound in Technology, Medicine and the Environment
22
Why is gel put between an ultrasound probe and the skin?
Sound in Technology, Medicine and the Environment
23
Announcements in a school gymnasium are hard to understand. What would help most?
Sound in Technology, Medicine and the Environment
24
Moving away from a machine reduces the sound intensity to one hundredth of its original value. By how many decibels does the level fall?
dB
Sound in Technology, Medicine and the Environment
25
Order these spaces from the shortest reverberation time to the longest.
1. 1Classroom with carpet, ceiling tile and people
2. 2Bare concrete-block gymnasium
3. 3Concert hall designed for orchestral music
4. 4Recording studio, heavily treated

Endless drill

Fresh numbers every time, for the calculation questions in this unit.

Endless drillnew numbers every time

Generating a problem…