← ACARA Digital Technologies Years 7–8

A sound as a sequence of numbers

An ordered list of whole numbers, each measuring a sound's volume at a regular time. Plot them in order and join the dots to redraw an approximation of the wave.

Part of: ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 50

Understanding A sound as a sequence of numbers in ACARA Digital Technologies Years 7–8

What it does: Plotting every sample in its recorded order and joining the points rebuilds a wave that looks like the original. The first list rises then falls, but the second starts at its peak. The numbers are the same, yet the shape is different. Sampling turns a sound into a list of integers. Each number is one volume measurement. The position in the list tells you when the measurement was taken. Shuffle the list and you get a different wave. Reading a list of sample values means finding the biggest and smallest numbers. They show the peaks and dips of the wave.

Common mistakes: Lists start counting at index 0, so the first sample is samples[0]. samples[1] is the second sample. It should be first = samples[0]. The list has 5 samples, so the indexes run from 0 to 4. samples[n] is index 5, which does not exist and causes an error. It should be samples[n - 1].

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Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

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This module's key terms are also in a printable crossword (Modules 153–172) and word search (Modules 153–188).

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Learning
Duo
A digital sound is stored as 0, 40, 80, 40, 0. What kind of data is this?
An ordered list of whole numbers (samples)A picture of the wave saved as a drawing
Matches
plot([5, 0, 9, 0, 5])
↓
The samples were recorded as 0, 5, 9, 5, 0 but plotted in a mixed-up order, so the wave shape is lost. Plot them in the recorded order.
Applying
Meanings
Term
sample sequence
Meaning
An ordered list of whole numbers, each measuring a sound's volume at a regular time. Plot them in order and join the dots to redraw an approximation of the wave.
Practice
samples = [0, 40, 70, 40, 0, -40, -70, -40]
Testing
Gaps
print(samples[])
Check Answer
Spots
1samples = [0, 5, 9, 5, 0, -5]
2first = samples[1]

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Quick Questions

1. A digital sound is stored as 0, 40, 80, 40, 0. What kind of data is this?
A. A picture of the wave saved as a drawing
B. An ordered list of whole numbers (samples) ✓
Sampling turns a sound into a list of integers. Each number is one volume measurement.
2. You plot the samples 0, 40, 80, 40, 0 in order and join the dots. What do you get?
A. An approximation of the sound wave ✓
B. A perfect copy of the original wave
Joining the sample points redraws the wave, but only as an approximation, because the gaps between samples are missing.
3. Which statement about the order of samples is true?
A. Order matters, because each number is a measurement at a set time ✓
B. Order does not matter, because the numbers are the same
The position in the list tells you when the measurement was taken. Shuffle the list and you get a different wave.
4. The samples 10, 50, 90, 50, 10 are shuffled to 90, 10, 50, 10, 50. What happens to the plotted wave?
A. It has the same shape, because the numbers are the same
B. It has a different shape, so the sound changes ✓
The same numbers in a different order make a different wave and a different sound.
5. In the list 0, 30, 60, 30, 0, which sample is the highest volume measurement?
A. 60, the third sample ✓
B. 0, the first sample
Reading a list of sample values means finding the biggest and smallest numbers. They show the peaks and dips of the wave.

Match the Pairs

samples = [0, 5, 9, 5, 0, -5] → A sample sequence of six whole numbers: the wave rises to a peak of 9, falls back to 0, then drops below the middle line.
samples[0] → The first sample in the list. Counting starts at 0, so this is one volume measurement at the very start of the sound.
Plotting the samples in order and joining the dots redraws an approximation of the sound wave. → plot(samples) # join the dots in order
Order matters: the same numbers in a different order make a different wave. → [2, 8, 2] is not [8, 2, 2]
plot([5, 0, 9, 0, 5]) → The samples were recorded as 0, 5, 9, 5, 0 but plotted in a mixed-up order, so the wave shape is lost. Plot them in the recorded order.
samples = [0, 4.5, 9, 4.5, 0] → Samples are whole numbers (integers), so 4.5 is not allowed. Each measurement is rounded to a whole number, such as 4 or 5.

Key Term

sample sequence
An ordered list of whole numbers, each measuring a sound's volume at a regular time. Plot them in order and join the dots to redraw an approximation of the wave.

Fill in the Blanks

1. samples = [2, 6, 9, 6, 2] print(samples[0])
Hint: Type the index position of the first sample in the list.
2. samples = [4, 8, 4, 0, 4] count = len(samples)
Hint: Type the built-in function that counts how many items are in a list.
3. samples = [1, 5, 9, 5, 1] for s in samples: plot(s)
Hint: Type the keyword that steps through the list one item at a time, in order.
4. for i in range(len(samples)): plot(i, samples[i])
Hint: Type the loop variable that picks each sample by its position, so the order is kept.
5. samples = [0, 4, 8, 4, 0] if samples[0] == 0: print("starts silent")
Hint: Type the operator that checks whether two values are equal.

Spot the Error

Question 1
A samples = [0, 5, 9, 5, 0, -5]
B first = samples[1]
C print(first)
Line B — Lists start counting at index 0, so the first sample is samples[0]. samples[1] is the second sample. It should be first = samples[0].
Question 2
A samples = [2, 6, 9, 6, 2]
B n = len(samples)
C last = samples[n]
Line C — The list has 5 samples, so the indexes run from 0 to 4. samples[n] is index 5, which does not exist and causes an error. It should be samples[n - 1].
Question 3
A samples = [0 4 8 4 0]
B for s in samples:
C print(s)
Line A — The sample values in a list must be separated by commas. Without commas the list is not valid. It should be samples = [0, 4, 8, 4, 0].
Question 4
A s = [1, 4, 9, 6, 2]
B t = [0, 1, 2, 3, 4]
C for i in range(5):
D print(t[i], s[4 - i])
Line D — Each sample must be paired with its own time step, in order. s[4 - i] reads the samples backwards, so the wave would be drawn reversed. It should be print(t[i], s[i]).
Question 5
A s = [3, 7, 2, 8]
B points = []
C for i in range(len(s)):
D points.append((s[i], i))
Line D — When plotting a wave, time (the position in the sequence) goes on the x-axis and the sample value goes on the y-axis. The point has x and y swapped. It should be (i, s[i]).

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