Section 1 of 15Transverse & Longitudinal Waves
Transverse & Longitudinal
- Transverse & Longitudinal Transverse & Longitudinal Waves Transverse Waves Waves can exist as one of two types:
Transverse waves Longitudinal
- Transverse waves Longitudinal Transverse waves Longitudinal waves Transverse waves Transverse waves are defined as:
Waves which vibrate
- Waves which vibrate Waves which vibrate at right angles to the direction of energy transfer Transverse waves:
vibrate perpendicular (at
- vibrate perpendicular (at vibrate perpendicular (at right angles) to the direction of travel transfer energy,
- but not matter can exist as mechanical waves,
- (the particles of the medium)
- which can move in solids and on the surfaces of liquids but not inside liquids or gases can exist as electromagnetic waves,
- which can move in solids, liquids, gases,
- and in a vacuum On a transverse wave:
- but not matter can exist as mechanical waves,
the highest point
- the highest point the highest point above the rest position is called a peak or crest the lowest point below the rest position is called a trough Example of a transverse wave Transverse waves can be demonstrated on a rope when it is moved quickly up and down Examples of transverse waves are:
ripples on the
- ripples on the ripples on the surface of water vibrations on a guitar string S-waves (a type of seismic wave) electromagnetic waves (such as radio, light, X-rays, etc) Representing transverse waves Transverse waves are drawn as a single continuous line, usually with a central line showing the undisturbed position The curves are drawn so that they are perpendicular (at 90 degrees) to the direction of energy transfer These represent the peaks and troughs Transverse wave crests and troughs Transverse waves are represented as a continuous solid line with crests and troughs Longitudinal Waves Longitudinal waves are defined as:
Section 2 of 15Describing Wave Motion
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Describing Wave Motion When describing wave motion, there are several terms which are important to know, including:
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amplitude wavelength frequency period Amplitude Amplitude is defined as:
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The distance from the undisturbed position to the peak or trough of a wave It is given the symbol A and is measured in metres (m) On a graph where the vertical axis is displacement, amplitude is measured from the undisturbed position to either the highest point of the wave (peak) or the lowest point (trough) Wavelength Wavelength is defined as:
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The distance from one point on the wave to the same point on the next wave In a transverse wave:
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can be measured from one peak to the next peak In a longitudinal wave:
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can be measured from the centre of one compression to the centre of the next Wavelength is given the symbol λ (lambda) and is measured in metres (m) On a graph where the horizontal axis is distance, the wavelength can be determined by measuring the distance from one point on the wave to the same point on the next wave Using a graph to determine wavelength and amplitude Diagram showing the amplitude and wavelength of a wave Frequency Frequency is defined as:
Section 3 of 15The Wave Equation
The Wave Equation
The Wave Equation
- The Wave Equation The Wave Equation Wave speed is defined as:
The distance travelled
- The distance travelled The distance travelled by a wave each second Wave speed is given the symbol v and is measured in metres per second (m/s) Wave speed is the speed at which energy is transferred through a medium Transverse and longitudinal waves both obey the wave equation:
v = wave
- v = wave v = wave speed in metres per second (m/s) f = frequency in Hertz (Hz) λ = wavelength in metres (m) The wave speed equation may need to be rearranged,
- which can be done using this formula triangle:
Worked Example A
- Worked Example A Worked Example A wave in a pond has a speed of 0.15 m/s and a time period of 2 seconds.
- Calculate:
a) The frequency
- a) The frequency a) The frequency of the wave b) The wavelength of the wave Answer:
Part (a) Step 1
- Part (a) Step 1 List the known quantities Time period, T = 2 s Step 2: Write out the equation relating time period and frequency Step 3: Rearrange for frequency, f,
- and calculate the answer f = 1 ÷ T = 1 ÷ 2 Frequency, f = 0.5 Hz Part (b) Step 1: List the known quantities Wave speed, v = 0.15 m/s Frequency, f = 0.5 Hz Step 2: Write out the wave speed equation v = f × λ Step 3: Rearrange the equation to calculate the wavelength λ = v ÷ f Step 4: Use the frequency you calculated in part (a) and put the values into the equation λ = 0.15 ÷ 0.5 Wavelength, λ = 0.30 m Examiner Tips and Tricks When stating equations make sure you use the right letters:
Section 4 of 15Measuring the Speed of Waves
Measuring the Speed
- Measuring the Speed Measuring the Speed of Waves Experiments to Determine the Speed of Sound There are several experiments that can be carried out to determine the speed of sound Three methods are described below The apparatus for each experiment is given in bold Method 1: Measuring Sound Between Two Points Measuring the speed of sound directly between two points 1.
- Two people stand a distance of around 100 m apart 2.
- The distance between them is measured using a trundle wheel 3.
- One person has two wooden blocks, which they bang together above their head 4.
- The second person has a stopwatch which they start when they see the first person banging the blocks together and stops when they hear the sound 5.
- This is then repeated several times and an average value is taken for the time 6.
- The speed of sound can then be calculated using the equation:
Method 2
- Method 2 Using Echoes Measuring the speed of sound using echoes 1.
- A person stands about 50 m away from a wall (or cliff) using a trundle wheel to measure this distance 2.
- The person claps two wooden blocks together and listens for the echo 3.
- The person then starts to clap the blocks together repeatedly, in rhythm with the echoes 4.
- A second person has a stopwatch and starts timing when they hear one of the claps and stops timing 20 claps later 5.
- The process is then repeated and an average time calculated 6.
- The distance travelled by the sound between each clap and echo will be (2 × 50) m 7.
- The total distance travelled by sound during the 20 claps will be (20 × 2 × 50) m 8.
- The speed of sound can be calculated from this distance and the time using the equation:
Method 3
- Method 3 Using an Oscilloscope Measuring the speed of sound using an oscilloscope 1.
- Two microphones are connected to an oscilloscope and placed about 5 m apart using a tape measure to measure the distance 2.
- The oscilloscope is set up so that it triggers when the first microphone detects a sound,
- and the time base is adjusted so that the sound arriving at both microphones can be seen on the screen 3.
- Two wooden blocks are used to make a large clap next to the first microphone 4.
- The oscilloscope is then used to determine the time at which the clap reaches each microphone and the time difference between them 5.
- This is repeated several times and an average time difference calculated 6.
- The speed can then be calculated using the equation:
Measuring Wave Speed
- Measuring Wave Speed Measuring Wave Speed in Water Creating ripples in water 1.
- Choose a calm flat water surface such as a lake or a swimming pool 2.
- Two people stand a few metres apart using a tape measure to measure this distance 3.
- One person counts down from three and then disturbs the water surface to create a ripple 4.
- (using their hand, for example)
- The second person then starts a stopwatch to time how long it takes for the first ripple to get to them 5.
- The experiment is then repeated 10 times and an average value for the time is calculated 6.
- The average time and distance can then be used to calculate the wave speed using the equation:
Worked Example Small
- Worked Example Small Worked Example Small water waves are created in a ripple tank by a wooden bar.
- The wooden bar vibrates up and down hitting the surface of the water.
- The diagram below shows a cross-section of the ripple tank and water.
a) The amplitude
- a) The amplitude a) The amplitude of a water wave?
Section 5 of 15Transmission of Sound Waves
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Transmission of Sound Waves Sound waves are longitudinal waves They transfer energy by the molecules vibrating and knocking into neighbouring molecules The more molecules that are present the faster the wave can transfer energy, therefore:
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Sound waves travel fastest in solids Sound waves travel slowest in gases When sound waves move from one medium to another, there will be changes to their:
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Wave speed Wavelength The frequency of a sound wave does not change when it moves from one medium to another The relationship between the wave speed, wavelength and frequency can be determined using the wave equation This change in velocity can also result in a change of direction of the sound wave This phenomenon is also known as refraction Refraction of Sound When sound moves from a denser medium to a less dense medium:
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The wavelength of the sound wave decreases The frequency of the sound wave stays the same The velocity of the sound wave decreases When sound moves from a less dense medium to a denser medium:
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The wavelength of the sound wave increases The frequency of the sound wave stays the same The velocity of the sound wave also increases The speed of sound in air is also affected by temperature On warm days, air molecules move faster, hence they carry sound waves faster, increasing the speed of sound On cold days, air molecules move at a slower pace, so they carry sound waves at a slower pace, decreasing the speed of sound
Section 6 of 15Required Practical: Measuring Wave Properties
Required Practical: Measuring Wave Properties
Required Practical 8
- Required Practical 8 Measuring Wave Properties Equipment List Resolution of measuring equipment:
Metre ruler =
- Metre ruler = Metre ruler = 1 mm Stopwatch = 0.01 s Signal generator ~ 10 nHz Experiment 1: Water Waves in a Ripple Tank Aims of the Experiment To measure frequency, wavelength and wave speed by observing water waves in a ripple tank Variables Independent variable = frequency, f Dependent variable = wavelength, λ Control variables:
Same depth of
- Same depth of Same depth of water Same temperature of water Method Set up of ripple tank to investigate wave properties 1.
- Set up the apparatus as shown and fill the ripple tank with water to a depth of no more than 1 cm 2.
- Turn on the power supply and the light source to produce a wave pattern on the screen 3.
- The wavelength of the waves can be determined by using a ruler to measure the length of the screen and dividing this distance by the number of wavefronts 4.
- The frequency can be determined by timing how long it takes for a given number of waves to pass a particular point and dividing the number of wavefronts by the time taken 5.
- Record the frequency and wavelength in a table and repeat the measurements An example of the data collection table is shown below:
Analysis of Results
- Analysis of Results Analysis of Results The speed of the waves can be determined using the equation:
Wave Speed =
- Wave Speed = Wave Speed = Frequency × Wavelength v = f λ Where:
v = wave
- v = wave v = wave speed in metres per second (m/s) f = frequency in Hertz (Hz) λ = wavelength in metres (m) Experiment 2: Investigating Waves in a Solid Aim of the Experiment To measure frequency, wavelength and wave speed by observing waves in a solid object,
- such as a stretched string or elastic cord Variables Independent variable = frequency, f Dependent variable = wavelength, λ Control variables:
Section 7 of 15Reflection, Absorption & Transmission
Reflection, Absorption &
- Reflection, Absorption & Reflection, Absorption & Transmission Depending on the densities of the materials on either side of a boundary, a wave may be:
Reflected Transmitted Absorbed
- Reflected Transmitted Absorbed Reflected Transmitted Absorbed Reflection Reflection occurs when:
A wave hits
- A wave hits A wave hits a boundary between two media and does not pass through, but instead stays in the original medium The law of reflection states:
The angle of
- The angle of The angle of incidence = The angle of reflection Reflection of a wave at a boundary Some of the wave may also be absorbed or transmitted Echos are examples of sound waves being reflected off a surface Flat surfaces are the most reflective The smoother the surface, the stronger the reflected wave is Rough surfaces are the least reflective This is because the light scatters in all directions Opaque surfaces will reflect light which is not absorbed by the material The electrons will absorb the light energy,
- then reemit it as a reflected wave Transmission Transmission occurs when:
A wave passes
- A wave passes A wave passes through a substance For light waves, the more transparent the material, the more light will pass through Transmission can involve refraction but is not exactly the same For the process to count as transmission, the wave must pass through the material and emerge from the other side When passing through a material, waves are usually partially absorbed The transmitted wave may have a lower amplitude because of some absorption For example, sound waves are quieter after they pass through a wall When a wave passes through a boundary it may be absorbed and transmitted Absorption Absorption occurs when:
Energy
- Energy is transferred from the wave into the particles of a substance Waves can be partially or completely absorbed Sound waves are absorbed by brick or concrete in houses Light will be absorbed if the frequency of light matches the energy levels of the electrons The light will be absorbed,
- and then reemitted over time as heat If an object appears red, this means:
Section 8 of 15Required Practical: Investigating Reflection & Refraction
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Investigating Reflection & Refraction Equipment List Resolution of measuring equipment:
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Protractor = 1° Ruler = 1 mm Experiment 1: Reflection of Light in a Mirror Aims of the Experiment To investigate specular reflection off a smooth surface Variables Independent variable = angle of incidence, i Dependent variable = angle of reflection, r Control variables:
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Distance of ray box from mirror Width of the light beam Same frequency / wavelength of the light Method Apparatus to investigate reflection 1. Set up the apparatus as shown in the diagram 2. In the middle of the paper use a ruler to mark a straight line of about 10 cm long 3. Use a protractor to draw a 90° line that bisects (cuts in half) the 10 cm line 4. Place the mirror on the first line as shown in the diagram above 5. Switch on the ray box and aim a beam of light at the point where the two drawn lines cross at an angle 6. Use the pencil to mark two positions of the light beam:
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A point just after leaving the ray box The point on the reflected beam about 10 cm away from the mirror 7. Remove the ray box and mirror 8. Use a ruler to join the two marked positions to the point where the originally drawn lines crossed 9. Use the protractor to measure the two angles from the 90° line. The angle for the ray towards the mirror is the angle of incidence, and the other the angle of reflection 10. Repeat the experiment three times with the beam of light aimed at different angles An example of the data collection table is shown below:
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Analysis of Results The law of reflection states:
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i = angle of incidence in degrees (°) r = angle of reflection in degrees (°) If the experiment was carried out correctly, the angles should be the same, as shown below:
Section 9 of 15Sound Waves
Sound Waves
Sound Waves in
- Sound Waves in Sound Waves in Solids Higher Tier Only Sound waves are vibrations of air molecules When a sound wave comes into contact with a solid those vibrations can be transferred to the solid For example, sound waves can cause a drinking glass to vibrate If the glass vibrates too much the movement causes the glass to shatter Sound is an example of a longitudinal wave, hence it consists of:
Compressions - regions
- Compressions - regions Compressions - regions of higher density Rarefactions - regions of lower density Sound is a longitudinal wave consisting of compressions and rarefactions - these are areas where the pressure of the air varies with the wave These compressions and rarefactions cause changes in pressure,
- which vary in time with the wave Therefore, sound is a type of pressure wave When the waves hit a solid, the variations in pressure cause the surface of the solid to vibrate in sync with the sound wave When sound waves hit a solid, the fluctuating pressure causes the solid to vibrate Sound Waves in the Ear Higher Tier Only Sound waves can be heard by human beings because sound waves are transferred from the air to the solid components of the ear In the case of the human ear, the sound waves are transferred by two main solid components:
The eardrum which
- The eardrum which is made of tissue and skin Three small bones The sound wave travels down the auditory canal towards the eardrum The pressure variations created by the sound wave exert a varying force on the eardrum causing it to vibrate The vibration pattern of the sound waves creates the same pattern of vibration in the eardrum The eardrum vibration is transferred to the three small bones The vibration of these small bones then transfers the vibrations to the inner ear In the inner ear, nerve cells detect the sound and send a message to the brain giving the sensation of sound The human ear is made up of several components which turn sound waves into signals which the brain can interpret The transmission of sound to the human ear only works over a limited range of frequencies This limits the range of sound frequencies a human can hear The range of frequencies a human can hear is 20 Hz to 20 000 Hz
Section 10 of 15Exploring Structure Using Waves
Core Concept
- Core Concept Fundamental syllabus principles and theoretical foundations.
Process & Behavior
- Process & Behavior Key physical or chemical mechanisms, properties, and interactions.
Key Application
- Key Application Exam requirements, real-world examples, and industrial relevance.
Section 11 of 15Ultrasound
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Ultrasound crack detection to find cracks in rail tracks Reflection seismology to detect oil and gas underground Seismic activity (Earthquakes) can be used to investigate the structure of the Earth The properties of a substance that allow the detection of hidden structures are:
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Reflection Absorption Transmission The speed of sound in the substance Each type of substance will produce different amounts of reflection, absorption and transmission Each type of substance will also transmit a sound wave at a specific speed Sounds will travel faster in solids than liquids and sound travels faster in liquids than gases Certain structures will reflect a proportion of the sound wave and transmit the rest Some substances will absorb sound waves with very little reflection By detecting the amount of sound reflected and the speed of the wave the hidden structure can be identified Ultrasound Ultrasound Higher Tier Only Ultrasound is defined as:
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Sound waves with a frequency above the human hearing range of 20 000 Hz The human ear can hear frequencies between 20 Hz and 20 000 Hz The human ear can detect sounds between around 20 and 20 000 Hz in frequency with a peak sensitivity at around 4000 Hz When meeting a boundary between two media ultrasound may be:
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Partially reflected Partially transmitted Partially absorbed The percentage that is reflected or transmitted depends on the two media at the boundary An air and glass boundary will have different percentages compared to an air and wall boundary The percentage of the wave reflected is greatest when the difference in speed of sound between the media is large For example, when sound in air hits a brick boundary, most of the sound is reflected because waves travel much faster in brick than in air
Section 12 of 15Echo Sounding
Echo Sounding
Echo Sounding Higher
- Echo Sounding Higher Echo Sounding Higher Tier Only Echo sounding uses ultrasound to detect objects underwater The sound wave is reflected off the ocean bottom The time it takes for the sound wave to return is used to calculate the depth of the water The distance the wave travels is twice the depth of the ocean This is the distance to the ocean floor plus the distance for the wave to return Echo sounding is used to determine water depth Worked Example The sound wave released from a ship took 0.12 seconds to return.
- The speed of sound in water is 1500 m/s.
What was the
- What was the What was the depth of the sea?
Step 1
- Step 1 List the known quantities Wave speed, v = 1500 m/s Time, t = 0.12 s Step 2: Write out the wave speed, distance and time formula Step 3: Rearrange the equation to make distance (x) the subject x = v × t Step 4: Put known values into the equation x = 1500 × 0.12 = 180 m Step 5: Half the distance to obtain the depth d = 180 ÷ 2 Depth, d = 90 m Examiner Tips and Tricks Don't forget to take into account that the sound wave has travelled twice the distance.
You
- You can do this one of two ways:
Halve the time
- Halve the time Halve the time at the beginning, or Halve the distance at the end
Section 13 of 15Ultrasound in Medical & Industrial Imaging
Ultrasound in Medical
- Ultrasound in Medical Ultrasound in Medical & Industrial Imaging Higher Tier Only When ultrasound reaches a boundary between two media, some of the waves are partially reflected The remainder of the waves continue through the material and are transmitted Ultrasound transducers are able to:
Emit ultrasound Receive
- Emit ultrasound Receive Emit ultrasound Receive ultrasound The time taken for the reflections to reach a detector can be used to determine how far away a boundary is This is because ultrasound travels at different speeds through different media This is by using the speed, distance, time equation Where:
v = speed
- v = speed v = speed in metres per second (m/s) s = distance in metres (m) t = time in seconds (s) This allows ultrasound waves to be used for both medical and industrial imaging Ultrasound in Medicine In medicine, ultrasound can be used:
To construct images
- To construct images To construct images of a foetus in the womb To generate 2D images of organs and other internal structures (as long as they are not surrounded by bone) As a medical treatment such as removing kidney stones An ultrasound detector is made up of a transducer that produces and detects a beam of ultrasound waves into the body The ultrasound waves are reflected back to the transducer by boundaries between tissues in the path of the beam For example, the boundary between fluid and soft tissue or tissue and bone When these echoes hit the transducer, they generate electrical signals that are sent to the ultrasound scanner Using the speed of sound and the time of each echo’s return, the detector calculates the distance from the transducer to the tissue boundary By taking a series of ultrasound measurements, sweeping across an area, the time measurements may be used to build up an image Unlike many other medical imaging techniques, ultrasound is non-invasive and is believed to be harmless Ultrasound can be used to construct an image of a foetus in the womb Ultrasound in Industry In industry, ultrasound can be used to:
Check for cracks
- Check for cracks Check for cracks inside metal objects Generate images beneath surfaces A crack in a metal block will cause some waves to reflect earlier than the rest,
- so will show up as pulses on an oscilloscope trace Each pulse represents each time the wave crosses a boundary The speed of the waves is constant,
- so measuring the time between emission and detection can allow the distance from the source to be calculated Ultrasound is partially reflected at boundaries,
- so in a bolt with no internal cracks, there should only be two pulses Worked Example In the diagram above, a very high-frequency sound wave is used to check for internal cracks in a large steel bolt.
- (at the start and end of the bolt)
- The oscilloscope trace shows that the bolt does have an internal crack.
- Each division on the oscilloscope represents a time of 0.000002 s.
The speed of
- The speed of The speed of sound through steel is 6000 m/s.
Section 14 of 15Seismic Waves
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Seismic Waves Higher Tier Only Earthquakes produce two types of waves:
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P-waves (primary waves) S-waves (secondary waves) These waves pass through the Earth’s centre and can be detected at various points around the Earth using seismometers By carefully timing the arrival of the waves at each point, the location of the earthquake, along with its magnitude, can be pinpointed P-Waves P-waves are longitudinal waves These waves can pass through solids and liquids P-waves are faster than S-waves They are very low frequency sound waves known as infrasound Infrasound is any sound below the frequency of human hearing (<20 Hz) The waves refract as they pass through the different layers of the Earth This refraction affects the regions in which waves can be detected, yielding important information about the nature and size of the Earth’s various layers Low frequency sound waves (P-waves) produced by earthquakes, pass through the centre of the Earth, revealing useful information about its structure S-Waves S-waves are a type of transverse wave Unlike P-waves, S-waves are unable to travel through liquids They pass through solids only S-waves are slower than P-waves This means that they are unable to travel through the Earth’s molten (liquid) outer core – providing important evidence about its state and size Transverse S-Waves are unable to pass through the Earth’s liquid outer core Discoveries from Seismic Waves Higher Tier Only The interior of the Earth is not directly observable as it is not physically possible to drill that far The furthest humans have managed to drill down is 12.2 km - whereas the radius of the Earth is over 6000 km!
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Examiner Tips and Tricks This topic covers the properties of longitudinal and transverse waves, how waves travel through different mediums, wave speed, and refraction, so its the perfect place to consolidate your conceptual understanding.
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Students often struggle to remember the differences between S-waves and P- waves, so try writing out the following:
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S-waves = Secondary waves (arrive second) slower speed, transverse, go through solids only From this, you can remember that P-waves are primary waves (they arrive first), faster speed, they are longitudinal, they go through liquids as well as solids.
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Seismic waves provide vital evidence that has led to a greater understanding of the structure of the Earth The two main discoveries are:
Section 15 of 15Exam Checklist & Tips
Specification Mastery Checklist
- Key Definitions Ensure precise recall of terms and units as required by examination mark schemes.
- Equations & Formulas Double-check balanced state symbols, subscripts, and SI unit conversions.
- Common Misconceptions Verify experimental conditions, controls, and comparative trends across groups.