How waves are reflected, how ultrasound is used for scans and echo sounding, how to work out a distance from an echo, and what seismic waves tell us about the Earth. Separate Physics only.
Objectives
State and use the law of reflection, measuring angles from the normal.
Explain the difference between reflection from a smooth surface and a rough surface.
Describe how ultrasound is used for imaging and for echo sounding.
Calculate distance using distance = speed × time ÷ 2 for an echo.
Higher tier: describe P and S waves and explain what they tell us about the structure of the Earth.
Reflection, ultrasound and seismic waves explained
Start here
A bat flies through a dark cave without hitting the walls, even though it can hardly see. It squeaks, listens for the echo that comes back, and works out where everything is. Dolphins do the same trick underwater, and so do ships that need to know how deep the sea is.
Doctors use a similar idea to look at a baby inside its mother, and scientists use waves from earthquakes to learn what is inside the Earth. In every case a wave goes out, bounces back, and the way it comes back, including how long it takes, tells us something we could not see directly. That is what detection means in this topic.
Think of shouting into a valley and waiting for the answer to come back. A long wait means the far side is a long way away, and a short wait means it is close. That waiting time is the information, and you will turn it into a distance with one short equation.
This lesson is for separate Physics, so you may not need it if you are doing combined science. It covers the law of reflection, smooth and rough surfaces, ultrasound, echo calculations and seismic waves. The seismic waves part is Higher tier, and it is marked that way when you reach it.
By the end you will be able to do three things. First, state and use the law of reflection. Second, describe how ultrasound is used to make pictures and to measure depth, and calculate a distance from an echo time. Third, if you are working at Higher tier, describe P waves and S waves and what they tell us about the Earth.
A flow of four boxes. A wave is sent out, it hits something, it bounces back, and the echo is read to find out about the thing it hit.
The law of reflection
When a wave hits a boundary, which is the edge between two materials, some of it can bounce back, and the rest can carry on or be absorbed. This is reflection. Light reflects from a mirror, and sound reflects from a wall, a cliff or the inside of a tunnel.
To describe reflection we draw a dotted line at right angles to the surface, called the normal. The angle of incidence is the angle between the incoming ray and the normal. The angle of reflection is the angle between the bounced ray and the normal.
The law of reflection says that the angle of incidence equals the angle of reflection. If a ray hits a mirror at 35° to the normal, it bounces off at 35° to the normal on the other side. The incoming ray, the normal and the bounced ray all lie in the same flat plane.
Always measure from the normal and not from the surface. This is the mistake that costs the most marks in this topic, so check it twice before you move on. If a question gives you the angle between the ray and the mirror, subtract it from 90° to get the angle to the normal, so a ray at 20° to the mirror has an angle of incidence of 70°.
Think of a tennis ball bouncing off a wall. If you throw it at a steep angle it leaves at a steep angle, and if you throw it at a shallow angle it leaves at a shallow angle. Waves behave in the same fair way, and the law of reflection is the rule that describes it.
A ray of light hitting a flat mirror. A dotted normal line stands at right angles to the mirror. The incoming ray and the reflected ray make equal angles with the normal, marked i and r.
Smooth and rough surfaces
The law of reflection works for every surface, but the result looks very different on a smooth surface and a rough one. A smooth surface, such as a mirror or still water, has all its tiny surfaces pointing the same way. Parallel rays hitting it all bounce off in one direction, and you see a clear picture, like your own face in a mirror or the sky in a still lake.
A rough surface, such as a sheet of paper or a wall, is covered in tiny bumps that point in different directions. Each ray still obeys the law of reflection, but because the normals point every which way, the rays scatter in many directions. This is called diffuse reflection.
Diffuse reflection is the reason you can read this page, or a whiteboard, from any seat in a room. Light scatters off the paper in all directions, so some of it always reaches your eyes. If paper were a mirror, you would only see it from one place.
Sound reflects too. Hard, flat surfaces such as tiled walls reflect sound well, which is why a bathroom has echoes. Soft surfaces such as curtains, sofas and carpets absorb a lot of the sound, which means they take in its energy, so a furnished room sounds much quieter than an empty one. This is why a recording studio is lined with soft foam.
So, a rough surface does not break the law of reflection. Each tiny part of it still reflects at equal angles to its own normal, so the law is true everywhere. The overall effect is just a messy scatter instead of a neat beam, which is why we say the reflection is diffuse.
Ultrasound
Sound is a longitudinal wave, and humans can hear it only if its frequency is within a certain range. For most young people, the range is about 20 Hz to 20 000 Hz, and the top of the range drops as people get older. Sounds above or below that range are still sound waves, but we cannot hear them.
Ultrasound is sound with a frequency above 20 000 Hz, higher than humans can hear. Infrasound is the opposite, with a frequency below about 20 Hz. Think of a dog whistle, which makes a note you cannot hear but a dog can, because dogs can hear higher frequencies than people. Bats and dolphins use ultrasound to find their way around.
When ultrasound reaches a boundary between two different materials, some of it is reflected, and the rest carries on through. How much bounces back depends on the two materials. This partial reflection is what makes ultrasound so useful, because every boundary in the body or in a metal part sends back its own echo.
Ultrasound is also safe for living things. It is not ionising, which means it does not damage cells in the way that X-rays can, and the energy it carries is very small. That is why doctors can use it on an unborn baby, and why it is used for scans again and again without harm.
You do not need to learn lots of numbers here. Remember the hearing range, and remember that ultrasound is above it. If an exam question says 'a sound too high for humans to hear', the word they want is ultrasound.
Using ultrasound
In a hospital, a probe sends pulses of ultrasound into the body and listens for the echoes. Each time the pulse reaches a boundary between two kinds of tissue, such as a baby and the fluid around it, part of it bounces back. The pulses that return later have travelled further, so they came from deeper in the body.
A computer times each echo, works out how far it travelled and builds up a picture, called a scan, on a screen that the doctor can look at straight away. A gel is spread on the skin first. Without it, there would be a thin layer of air between the probe and the body, and most of the ultrasound would reflect at the skin instead of going in.
Ships use ultrasound for echo sounding. The ship sends a pulse down to the sea bed and times how long the echo takes to return. Because sound travels at about 1500 m/s in water, the time tells the crew how deep the water is, and it also warns them of rocks and shallow patches.
Ultrasound can also find cracks. A pulse sent into a metal part is partly reflected by any crack inside it, so a crack shows up as an extra echo that arrives earlier than the echo from the far side. This tells engineers a part is faulty without cutting it open, and the arrival time of the extra echo shows how deep the crack is.
The idea is the same every time. A pulse goes in, partial reflections come back, and the timing tells you where the boundaries are. Learn that one idea and you can explain any of these uses, whether it is a baby, a ship or a bridge support.
A flow of four boxes showing how an ultrasound scan works. A probe sends a pulse, the pulse reflects at a boundary, the echo returns to the probe, and a computer times it and builds a picture.
Echo calculations
An echo has travelled to the boundary and back, so the total distance covered is twice the distance to the boundary. This is the trap in every echo question. If you forget the halving, your answer is double what it should be, and you will lose a mark.
The equation is distance = speed × time ÷ 2. The speed is the speed of the sound in that material, and the time is the time for the echo to return, measured from the moment the pulse is sent. The ÷ 2 turns the there-and-back distance into the depth or the distance to the wall.
Sound travels at about 340 m/s in air and about 1500 m/s in water, because the particles in water are closer together and pass the vibration on faster. Use the number the question gives you, because the examiner has chosen the speed to make the answer come out neatly. If the question does not give one, use 340 m/s for air and 1500 m/s for water.
Here is an example in water. A boat sends an ultrasound pulse down, and the echo returns after 0.6 s. The total distance is 1500 × 0.6 = 900 m, so the depth is 900 ÷ 2 = 450 m. The sea bed is about half a kilometre below the boat.
Write your working in three short lines. First the equation, then the numbers substituted, then the answer with its unit. Check that the answer is half of the speed × time you worked out, and you will not forget the halving. A final glance at the unit, metres, finishes the job.
Bars showing an echo journey in metres. The sound goes 450 metres down, comes 450 metres back up, and covers 900 metres in total, so the depth is half of the total.
Seismic waves (Higher tier)
This step is Higher tier. An earthquake happens when rock suddenly slips along a crack deep underground, and it sends out waves through the Earth called seismic waves. Detectors all over the world record them, and by studying when and where they arrive, scientists can work out what is inside the Earth, which nobody can dig down to see.
There are two kinds. P waves are longitudinal, and they can travel through solids and through liquids, which makes them behave like sound waves. They also travel faster, so they arrive first, and the letter P is a reminder of the word primary.
S waves are transverse, and they can only travel through solids, so they cannot pass through a liquid. They are slower than P waves, so they arrive second, and the letter S is a reminder of the word secondary.
Detectors on the far side of the Earth from an earthquake pick up P waves, but not S waves. This tells us that something in the way blocks the S waves, and only a liquid does that. So the outer core of the Earth must be liquid, and the missing S waves are the evidence. In an exam, always say both parts: S waves cannot pass through liquids, and none arrive on the far side.
Waves also change speed and direction where one layer of the Earth meets another, in the same way that light changes direction when it enters glass. Scientists use these changes to work out where the boundaries between the layers are. Put together, the results show a solid crust and mantle, a liquid outer core and a solid inner core. That is a lot of knowledge from waves alone.
Recap
The law of reflection says the angle of incidence equals the angle of reflection, both measured from the normal, which is the line at right angles to the surface. A smooth surface reflects rays in one direction, and a rough surface scatters them in many directions, which is called diffuse reflection.
Ultrasound is sound above 20 000 Hz, which is higher than people can hear. It is partly reflected at boundaries and it is not ionising, so it can be used to image a baby or to find cracks in metal. Echo sounding uses the same idea to measure the depth of the sea.
For echoes, distance = speed × time ÷ 2, because the sound goes there and back. Sound travels at about 340 m/s in air and 1500 m/s in water. Always write the equation, substitute the numbers, and give the unit, and look out for the trick where the time is for the whole journey.
At Higher tier, P waves are longitudinal and travel through solids and liquids, and S waves are transverse and travel only through solids. S waves are not detected on the far side of the Earth, which shows that the outer core is liquid.
How this is asked in an exam: you may be given an echo time and a speed and told to find a depth, or you may be asked to explain why the time is halved. For the seismic part, you may be asked what the missing S waves tell us. Use short, clear sentences with the key words reflect, boundary, there and back, and liquid, and give a number only when the question asks for one.
Key points
The angle of incidence equals the angle of reflection, measured from the normal.
A rough surface scatters rays in many directions. This is diffuse reflection.
Ultrasound is sound above 20 000 Hz, and it is partly reflected at boundaries.
Echo distance = speed × time ÷ 2. Sound travels at about 340 m/s in air and 1500 m/s in water.
Higher tier: P waves go through solids and liquids, but S waves go only through solids.
Higher tier: no S waves on the far side of the Earth shows the outer core is liquid.
Worked examples
Example 1
A ray of light hits a mirror at an angle of incidence of 40°. State the angle of reflection.
The law of reflection says the angle of incidence equals the angle of reflection.
Both angles are measured from the normal, which is the line at right angles to the mirror.
So the angle of reflection is 40°.
Answer: 40°
Common slips
Slip: The two angles add up to 90°, so the angle of reflection is 50° The angles are equal to each other. They do not have to add to 90°.
Slip: Measure the angles from the mirror surface The angles are measured from the normal, not from the surface.
Slip: The angle of reflection is 80° It is 40°, not double the angle of incidence.
Example 2
A ship sends an ultrasound pulse to the sea bed. The echo returns after 0.4 s. Sound travels at 1500 m/s in water. Work out the depth.
The pulse travelled down and back, so the total distance is twice the depth.
Use distance = speed × time ÷ 2.
Substitute the numbers: 1500 × 0.4 ÷ 2 = 300 m.
Answer: 300 m
Common slips
Slip: The pulse travelled only down It also came back up, so the time covers both journeys.
Slip: distance = speed ÷ time Multiply the speed by the time, then halve it.
Slip: 600 m That is the total distance there and back. The depth is half of it, 300 m.
Example 3
Higher tier. Explain how seismic waves show that part of the Earth's core is liquid.
S waves cannot travel through liquids, but they can travel through solids.
S waves are not detected on the far side of the Earth from an earthquake, while P waves are.
So something in the Earth must block S waves, and that is the liquid outer core.
Answer: S waves are not detected on the far side, and S waves cannot pass through liquids, so part of the core is liquid.
Common slips
Slip: P waves cannot travel through liquids P waves can travel through solids and liquids. It is the S waves that cannot pass through liquids.
Slip: S waves are detected everywhere They are missing on the far side, and that gap is the evidence.
Slip: The core is solid because P waves arrive P waves pass through solids and liquids, so their arrival does not show the core is solid.
Questions and answers
Reflection, ultrasound and seismic waves practice questions for GCSE Combined Science Physics. Try each one, then open the answer. Easy questions come first.
Question 1 Easy
A light ray hits a mirror at 25 degrees to the normal. State the angle of reflection.
Show answer
Answer: 25 degrees
The law of reflection.
The angles are equal, so 25 degrees.
Question 2 Easy
State the frequency above which sound is called ultrasound.
Show answer
Answer: above 20 000 Hz
Humans hear up to about 20 000 Hz.
Ultrasound is above 20 000 Hz.
Question 3 Easy
Name the type of seismic wave that cannot travel through liquids.
Show answer
Answer: S waves
One type is transverse.
S waves cannot pass through liquids.
Question 4 Easy
State the speed of sound in air, to the nearest 10 m/s.
Show answer
Answer: 340 m/s
Sound travels at about 340 m/s in air.
The answer is 340 m/s.
Question 5 Medium
An echo returns after 0.2 s in air where sound travels at 340 m/s. Work out the distance to the wall.
Show answer
Answer: 34 m
distance = speed × time ÷ 2
340 × 0.2 ÷ 2 = 34 m
Question 6 Medium
An ultrasound pulse returns from the sea bed after 0.08 s. Sound travels at 1500 m/s in water. Work out the depth.
Show answer
Answer: 60 m
distance = speed × time ÷ 2
1500 × 0.08 ÷ 2 = 60 m
Question 7 Medium
State what happens when ultrasound reaches a boundary between two different tissues.
Show answer
Answer: Some of it is reflected.
The tissues have different properties.
Some of the ultrasound is reflected.
Question 8 Medium
State one use of ultrasound.
Show answer
Answer: to image an unborn baby
It is safe for imaging.
It is used to image an unborn baby.
Exam-style questions
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
Exam-style question 14 marks
A ship uses ultrasound to measure the depth of the sea. A pulse returns after 0.4 s. The speed of sound in seawater is 1500 m/s.
(a) Explain why the depth is not 1500 × 0.4. [1 mark]
(b) Work out the depth of the sea. [2 marks]
(c) State what ultrasound is. [1 mark]
Show answer and marking points
Answer: (a) The pulse travels down and back, so the total distance is twice the depth. (b) 300 m (c) Sound with a frequency above 20 000 Hz.
(a) the pulse travels to the sea bed and back (1)
(b) 1500 × 0.4 ÷ 2 (1)
(b) 300 m (1)
(c) sound above 20 000 Hz (1)
Exam-style question 24 marks
After an earthquake, seismic waves are detected around the world.
(a) State the difference between P waves and S waves. [2 marks]
(b) Explain what the absence of S waves on the far side of the Earth shows about the core. [2 marks]
Show answer and marking points
Answer: (a) P waves are longitudinal and travel through solids and liquids, but S waves are transverse and travel only through solids. (b) S waves cannot pass through liquids, so the outer core must be liquid.
(a) P waves are longitudinal and travel through solids and liquids (1)
(a) S waves are transverse and travel only through solids (1)
(b) S waves cannot travel through liquids (1)
(b) so the outer core is liquid (1)
Common mistakes
Measuring the angle of reflection from the mirror surface
The angles of incidence and reflection are measured from the normal, the line at right angles to the surface.
Forgetting to halve the echo distance
The echo travels there and back, so use distance = speed × time ÷ 2.
Saying ultrasound can be heard
Ultrasound is above 20 000 Hz, which is higher than humans can hear.
Saying a rough surface breaks the law of reflection
Each tiny part still obeys the law, but the normals point in many directions, so the rays scatter. This is diffuse reflection.
Saying S waves pass through liquids
Higher tier. S waves travel only through solids. P waves travel through solids and liquids.
Questions students ask
Is Reflection, ultrasound and seismic waves on the Foundation or Higher tier?
Reflection, ultrasound and seismic waves is on both Foundation and Higher papers for GCSE Combined Science Physics, aimed at around grade 6.
What is a common mistake on Reflection, ultrasound and seismic waves?
Measuring the angle of reflection from the mirror surface. The angles of incidence and reflection are measured from the normal, the line at right angles to the surface.
Where are the answers to the Reflection, ultrasound and seismic waves questions?
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.