Oscilloscopes, Pitch and Loudness

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 3.26 — How an oscilloscope and microphone display a sound wave (bold P statement — Paper 2 only)
• 3.27 — Practical: investigate the frequency of a sound wave using an oscilloscope (bold P statement — Paper 2 only) (required practical)
• 3.28 — How the pitch of a sound relates to the frequency of vibration (bold P statement — Paper 2 only)
• 3.29 — How the loudness of a sound relates to the amplitude of vibration (bold P statement — Paper 2 only)

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

A MICROPHONE contains a thin diaphragm that is pushed and pulled by the changing air pressure of a sound wave, and it converts that motion into a changing electrical voltage. An OSCILLOSCOPE draws that voltage on a screen as a graph against time. Between them they let you see a sound.

Now the point that has to be settled before anything else, because it causes a misconception that survives for years. The trace on the screen is a smooth wave with crests and troughs, and it looks exactly like a transverse wave. It is not one. The screen is showing a GRAPH OF PRESSURE AGAINST TIME, not a picture of the wave in space. A crest is a moment of high pressure — a compression arriving — and a trough is a moment of low pressure, a rarefaction. Sound remains longitudinal: the air molecules are still vibrating back and forth along the direction the wave travels, and nothing anywhere is moving sideways. The display is a graph, not a map of where anything is.

Reading the trace — which feature means what

1. The HEIGHT of the trace from the middle line is the AMPLITUDE. A taller trace means a larger amplitude, which means a LOUDER sound.
2. The horizontal distance for one complete wave is the PERIOD, read off using the time base — the setting that says how many seconds or milliseconds each horizontal division represents.
3. The FREQUENCY is then found from f = 1 ÷ T. More waves squeezed into the same width of screen means a shorter period and a HIGHER frequency, which means a HIGHER-PITCHED sound.
4. So the two things you hear map onto the two dimensions of the screen: LOUDNESS is vertical, PITCH is horizontal.
5. Changing one does not change the other. Turning a note up makes the trace taller and no more closely spaced; playing a higher note squeezes the waves together without making them taller.

Think of it like a heart-rate monitor for the air

A hospital monitor draws a line that rises and falls, and nobody imagines the patient's blood is physically moving up and down across the screen. The height means pressure and the sideways direction means time — the display is a graph, and everyone reads it as one without being told. An oscilloscope trace of a sound is exactly the same kind of object: height is pressure, sideways is time. The reason people are misled by one and not the other is only that a sound trace happens to be a smooth repeating wave, and it looks like the pictures of transverse waves drawn earlier in the topic.

Finding a frequency from a trace

On an oscilloscope the time base is set to 2.0 ms per division. One complete wave occupies 4.0 divisions. Find the period and the frequency.

1. Period T = number of divisions × time per division = 4.0 × 2.0 ms = 8.0 ms.
2. Convert to seconds: 8.0 ms = 8.0 × 10⁻³ s = 0.0080 s.
3. f = 1 ÷ T = 1 ÷ 0.0080.
4. = 125 Hz.

Answer: A period of 8.0 ms and a frequency of 125 Hz — a low note, around the B below middle C.

The conversion to seconds is where most marks are lost. A time base is almost always given in milliseconds or microseconds per division, and f = 1 ÷ T requires the period in seconds. Leaving the period in milliseconds gives an answer a thousand times too small, which is worth noticing: a frequency of 0.125 Hz would be one wave every eight seconds, and no sound is anything like that slow.

One last idea, which explains something the specification does not require but every learner wonders about. If pitch is frequency and loudness is amplitude, why do a violin and a flute playing the same note at the same volume sound completely different? Because a real instrument does not produce a single pure frequency. It produces a FUNDAMENTAL, which sets the pitch, together with quieter OVERTONES at multiples of it — and the particular mixture is what makes an instrument recognisable. On an oscilloscope this shows as a trace that repeats at the fundamental's period but is not a simple smooth curve. The pitch and the loudness are on the screen exactly as this page describes; the character of the sound is in the shape.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

Statements 3.28 and 3.29 — the two relationships to state

• PITCH depends on FREQUENCY: a higher frequency of vibration gives a higher-pitched sound
• LOUDNESS depends on AMPLITUDE: a larger amplitude of vibration gives a louder sound
• On an oscilloscope trace, PITCH is read horizontally — more waves in the same width means higher pitch
• On the same trace, LOUDNESS is read vertically — a taller trace means a louder sound
• The two are INDEPENDENT: changing the volume does not change the pitch, and vice versa

Learn this definition · Time base

The oscilloscope setting that fixes how much time each horizontal division of the screen represents, for example 2 ms per division. It is needed to convert a distance on the screen into a period.

Statement 3.27 — finding a frequency from an oscilloscope trace

1. Count the horizontal divisions occupied by ONE complete wave.
2. Multiply by the time base setting to get the period.
3. Convert the period into SECONDS — milliseconds must be divided by 1000.
4. Calculate the frequency with f = 1 ÷ T.
5. Check the answer is a plausible audio frequency, between about 20 Hz and 20 000 Hz.

Required practical 3.27 — investigating the frequency of a sound wave

1. Connect a microphone to the input of an oscilloscope and switch the time base on.
2. Use a signal generator and loudspeaker to produce a steady note of known frequency, placed a fixed distance from the microphone.
3. Adjust the time base until between two and four complete waves are visible across the screen.
4. Count the horizontal divisions occupied by one complete wave, estimating the fraction of a division at each end.
5. Multiply by the time base setting to find the period, convert it to seconds, and calculate the frequency from f = 1 ÷ T.
6. Repeat for at least six different frequencies on the signal generator and compare the calculated values with the generator settings.

Variables

Independent (changed) — The frequency produced by the signal generator, in hertz
Dependent (measured) — The period measured from the trace, in seconds

Sources of error

The trace on the screen is not a picture of the wave

A. WHAT IT LOOKS LIKE: a transverse wave, with crests and troughs, because that is the shape of the line drawn.

B. WHAT IT IS: a graph of pressure against time. A crest is a moment of high pressure — a compression — and a trough is a rarefaction. The sound itself is still longitudinal.

How the trace changes when you change the sound

Model answer [4 marks]

An oscilloscope has a time base of 5.0 ms per division. One complete wave occupies 2.0 divisions. Calculate the frequency of the sound. [4]

The period is the number of divisions multiplied by the time base setting, so T = 2.0 × 5.0 = 10 ms. Converting to seconds, T = 0.010 s. The frequency is f = 1 ÷ T = 1 ÷ 0.010 = 100 Hz.

Model answer [3 marks]

Describe how the trace on an oscilloscope changes when a note is played more loudly at the same pitch. [3]

Playing the note more loudly means the source is vibrating with a larger amplitude, so the pressure variations in the sound wave are greater and the microphone produces a larger voltage. The trace on the screen therefore becomes taller — its amplitude increases. Because the pitch is unchanged, the frequency is unchanged, so the horizontal spacing of the waves stays exactly the same.

Not this: The oscilloscope trace shows that sound is a transverse wave, because it has crests and troughs.

This: The trace is a GRAPH of pressure against time, not a picture of the wave. A crest is a moment of high pressure — a compression arriving at the microphone. Sound is longitudinal.

Mark-losing trap. Convert the period to SECONDS before using f = 1 ÷ T. Milliseconds give an answer 1000 times too small.

Mark-losing trap. Pitch is FREQUENCY (horizontal); loudness is AMPLITUDE (vertical). Do not swap them.

Mark-losing trap. The trace is a graph, not a picture. Sound stays longitudinal however the screen looks.

Mark-losing trap. Count the divisions for ONE complete wave — from a point to the matching point on the next.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · State [1 mark] — A note is played more loudly without changing its pitch. What happens to the oscilloscope trace?
2. Grade 7 · State [2 marks] — An oscilloscope trace of a sound looks like a wave with crests and troughs. What does a crest on the trace represent?
3. Grade 8 · Calculate [4 marks] — An oscilloscope has a time base of 2.5 ms per division. One complete wave occupies 4.0 divisions. Calculate the frequency of the sound.
4. Grade 9 · Describe [6 marks] — Select every statement that belongs in a full-mark description of how to use an oscilloscope to find the frequency of a note from a signal generator.
5. 9+ · Analyse [6 marks] — A student looks at an oscilloscope trace of a sound and says: 'The trace has crests and troughs just like a water wave, so sound must be transverse after all — the textbook is wrong.' Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who took a musical note to pieces, and the one who first connected a pitch to a number. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Hermann von Helmholtz — the one who took a musical note to pieces

This page reduces sound to two quantities, pitch and loudness, and Helmholtz is the person who showed that a real note contains far more than that. In On the Sensations of Tone he established that an instrument produces a fundamental frequency together with a series of quieter overtones at multiples of it, and that the particular mixture is what makes a violin sound like a violin. He built resonators tuned to individual overtones to pick them out one at a time, decades before an oscilloscope could display the whole trace at once.

• “Why do two instruments playing the same note sound so different?”
• “What are overtones, and how did you detect them?”
• “How did you isolate one frequency out of a complicated sound?”
• “Is pitch really just the frequency of the vibration?”
• “What did you learn about the ear by studying music?”

Galileo Galilei — the one who first connected a pitch to a number

Statement 3.28 says pitch depends on frequency, and Galileo is the first person to have shown it. Scraping a chisel across a brass plate he noticed that the shriek it produced came with a row of fine ridges scored in the metal, and that a higher note left the ridges closer together — a pitch and a countable rate of vibration, connected for the first time. He extended it to strings, relating the note to the length, the tension and the thickness. Before that, pitch was a quality; after it, a quantity.

• “What did the marks on the brass plate tell you about the note?”
• “How can a pitch be counted rather than merely heard?”
• “What decides the note a plucked string produces?”
• “Why did nobody think of measuring sound before?”
• “Is a musical note a quality or a quantity?”

Then defend it

On Incandio a lesson is not finished when the questions come out right. You teach the idea back to Ember, an AI apprentice who asks the awkward question, and then you argue it against Hermann von Helmholtz in a structured debate marked against descriptors you can read before you enter. Learn it, teach it, then defend it — all three happen on this page once the app loads.

Carry on through the course

• Previous lesson: Sound Waves
• Next lesson: Energy Stores and Transfers
• What a Wave Is — Something crosses the room and nothing gets to the other side — the idea that makes the rest of the topic possible.
• The Wave Equation — Two equations that connect everything on the previous page — and one of them you could have worked out yourself.
• The Doppler Effect — Why an ambulance changes note as it passes — and why the siren itself never does.
• The Electromagnetic Spectrum — Seven names for one thing — and the two properties that change as you go along it.
• Uses and Dangers of Electromagnetic Radiation — Seven bands, seven jobs — and why the danger rises steadily as you move along the spectrum.
• All of Physics · Incandio Science