Reflection and diffraction of sound: the echo method and hearing around a barrier

The idea

Sound reflects from a large hard surface as a delayed copy of the original pulse, which times its own speed, and it spreads past edges and through openings by an amount set by the ratio of its wavelength to the size of the obstacle.

Safety card

What you need

• A large flat hard reflecting wall at least 4 m wide and 3 m high (a brick handball wall or a gymnasium end wall) with 50 m of clear level ground in front of it
• 50 m tape measure, pegs and marker tape; a pair of hardwood clapper boards or a starter's clap stick
• Laptop or phone recording at 44.1 kHz into Audacity or an equivalent editor that shows a sample-accurate time axis, with an external microphone on a stand at 1.5 m
• Signal generator or tone app driving a powered speaker that holds a steady level at 250 Hz and at 4000 Hz
• Calibrated sound-level meter reading dB(A) and dB(C), or a phone sound-level app checked against one before use
• Rigid barrier 1.2 m high by 2.4 m wide (18 mm plywood on a frame) and a second identical sheet, so the pair can be set edge to edge with a gap of 1.00 m or 0.20 m
• Two cardboard tubes 50 mm in diameter and 600 mm long mounted on a protractor board with a small speaker at one tube and the microphone at the other, and a smooth rigid reflector 600 mm square
• Thermometer reading to 0.5 degrees Celsius; vernier caliper; 30 m tape and pegs for marking a 15 degree grid of measurement points behind the barrier

How to do it

1. Record the air temperature to 0.5 degrees Celsius and compute the expected speed of sound from v = 331.3 + 0.606 T, with T in degrees Celsius.
2. Echo timing: measure 50.0 m out from the wall to within 0.10 m, stand on the mark with the microphone beside you, start recording and clap once. Repeat for ten claps with 2 s between them.
3. Read the delay between the onset of the direct clap and the onset of its echo to the nearest millisecond for each of the ten claps, take the mean, and compute v = 2d/t with an uncertainty from the spread of the ten readings and from the 0.10 m distance reading.
4. Repeat the whole timing at 25.0 m and confirm the delay halves.
5. Reflection angles: set the two tubes on the protractor board with their open ends 200 mm from the reflector, hold 4000 Hz steady in the source tube, and read the level at the receiving tube in 10 degree steps either side of the equal-angle position. Repeat with the source tube at 30 degrees and then 45 degrees to the reflector, three readings at each step.
6. Gap diffraction: set the two sheets edge to edge with a 1.00 m gap, place the speaker 1.0 m behind the gap on the axis, and measure the level 2.0 m in front of the gap at 0, 5, 10, 20, 40 and 80 degrees from the axis. Repeat at 250 Hz without touching the speaker's drive level, then repeat the pair with the gap reduced to 0.20 m.
7. Barrier shadow: stand the 1.2 m barrier midway between the speaker and the microphone with each 1.00 m from it at the same height, and record the level at 250 Hz and at 4000 Hz. Remove the barrier without moving anything else and record both levels again; the drop for each frequency is that frequency's insertion loss.
8. Raise the microphone until it sits on the straight line from the speaker over the barrier's top edge, repeat both frequencies, and compare the two insertion losses at that position.

What you should see

At 20.0 degrees Celsius the linear fit gives v = 343.4 m/s, so a clap 50.0 m from the wall returns its echo 0.2912 s later, which is 12 841 samples at 44.1 kHz and is separated cleanly in the editor. The learner knows the timing worked when 2d/t lands within 1 per cent of the temperature value; the uncertainty is 0.7 per cent for d read to 0.10 m and t to 2 ms, and the 25.0 m delay is 0.1456 s. The received level through the tubes peaks at the step nearest the equal-angle position at every source angle. Gap diffraction separates the two frequencies: at 250 Hz the wavelength is 1.37 m, larger than either gap, so no minimum exists and the tone is heard right across the forward half-space. At 4000 Hz the wavelength is 86 mm, and the far-field first minimum for the 1.00 m gap lies at 4.9 degrees, but that pattern forms only beyond about w squared over lambda, 11.6 m, from the gap; at 2.0 m, with the speaker only 1.0 m behind, the tone stays loud across the geometric beam the speaker throws through the gap, whose edge on the 2.0 m measuring arc lies at 39.5 degrees, and falls away sharply beyond it. Narrowing the gap to 0.20 m, where w squared over lambda is 0.47 m, spreads the 4000 Hz tone far beyond its 8.6 degree geometric beam, with its first minimum at 25.4 degrees. Behind the barrier the 4000 Hz tone falls much further than the 250 Hz tone at the same point. The model's knife-edge calculation for a 1.20 m barrier with source and microphone each 1.00 m away at the same height gives 19.3 dB at 250 Hz and 31.2 dB at 4000 Hz, a difference of 11.9 dB. Those figures use the small-angle form of nu, which overstates it when the edge stands 1.20 m above a line only 1.00 m from each side: the exact path difference of 1.124 m gives 18.3 dB and 30.1 dB, the same 11.9 dB apart. Measured outdoors both losses come out smaller still, and the difference smaller too, because reflections from the ground and from nearby walls fill the shadow and sound also passes round the two side edges of a sheet only 2.4 m wide, so the result to trust is the ordering and the size of the gap between the two frequencies rather than either figure on its own. With the microphone on the line of sight over the edge, theory gives 6.0 dB at both frequencies, since a half-plane halves the amplitude there whatever the wavelength.

What changes

What you change

frequency of the tone (250 Hz and 4000 Hz), then the gap width, then the distance to the reflecting wall

What you measure

sound level at each measurement point, and the echo delay

What you keep the same

• same speaker and the same drive level for both frequencies
• same microphone, stand height and recording gain
• source and microphone positions unmoved between the with-barrier and without-barrier readings
• air temperature recorded with every run
• same site, so the same reflecting surfaces are present throughout

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

• The echo is a new sound the wall makes; it is the same pulse arriving later after travelling to the wall and back.
• Only smooth polished surfaces reflect sound; any surface large compared with the wavelength reflects it, which is why rough brickwork returns a clear echo.
• Low notes and high notes travel at different speeds, so an echo would arrive smeared; in air every audible frequency travels at the same speed and a clap returns as a clap.
• Sound heard behind a barrier has passed through it; it has spread past the edge, and that is why the barrier removes the high frequencies far more than the low ones.
• Diffraction happens only at gaps narrower than a wavelength; it happens at every gap and is only wide-angled when the gap is about a wavelength across.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

• Physics Stage 6 Syllabus (2017), current: Year 11 until the end of 2026, Year 12 until Term 3 2027PH11-10PH11/12-3PH11/12-4PH11/12-5
• Physics 11-12 Syllabus (2025), not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027, first HSC examination 2028PY-11-02PY-11WS-03PY-11WS-04
• Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

1. www.nsw.gov.au/sites/default/files/noindex/2025-03/physics-stage-6-syllabus-2017.docx
2. education.nsw.gov.au/content/dam/main-education/teaching-and-learning/curriculum/key-learning-areas/science/s-6/physics/Physics-module-3-guide.docx
3. curriculum.nsw.edu.au/learning-areas/science/physics-11-12-2025/outcomes
4. hyperphysics.gsu.edu/hbase/Sound/diffrac.html