The shape of the lesson
By the end of the lesson, learners can
- Sampling the wave: In the lab, look at the smooth sound wave and the samples taken from it.
- Rate and resolution: Increase the sample rate in the lab, then the resolution.
- Sound file size: Each second stores (sample rate) samples, and each sample takes (resolution) bits.
- Sampling: the amplitude of the wave is measured at regular intervals and stored in binary.
- Sample rate: samples per second (Hz). Resolution: bits per sample.
- Higher either: more accurate recording, bigger file.
- Size: rate × resolution × seconds bits, then ÷ 8 and ÷ 1024 as needed.
One picture every idea returns to
A sound wave is sampled: its amplitude (height) is measured at regular intervals and each measurement is stored as a binary number. The sample rate is the number of samples taken in a second (in hertz, Hz). The sample resolution is the number of bits per sample. Increasing either one makes the recording more accurate (closer to the original sound) but increases the file size.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Sound in samples.. A sound wave changes smoothly and continuously, but a computer can only store separate binary numbers. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Sampling the wave | In the lab, look at the smooth sound wave and the samples taken from it. Project tab 2 of the lab (Sampling a sound wave) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Rate and resolution | Increase the sample rate in the lab, then the resolution. Project tab 2 of the lab (Sample rate and resolution) and let a student drive it while the class predicts. | Pairs |
| 21 to 30 min | Teach and check: Sound file size | Each second stores (sample rate) samples, and each sample takes (resolution) bits. Model the worked example Size of a recording on the board, one line at a time. Your turn: A 5-second sound has a sample rate of 1000 Hz and a resolution of 8 bits. How many bytes is it? | Corners |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 14 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Sound file size, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Corners
Put one answer or viewpoint in each corner of the room. Students move to the corner they agree with, justify the choice to a partner there, then hear one voice from each corner before the reveal.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Say what is measured: the amplitude (height) of the sound wave, at regular time intervals. "The sound is recorded in binary" is too vague for a mark. | Return to Sampling the wave: ask a pair to state the correct version and show it on the lab before moving on. |
| Doubling the resolution from 8 to 16 bits doubles the file size but gives 256 times as many levels (256 to 65 536). | Do not mix the two up. |
Representing sound: sample rate and resolution: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
Explain how a sound is converted into binary so that a computer can store it.
Define the terms sample rate and sample resolution.
A 4-second sound clip is recorded with a sample rate of 32 000 Hz and a sample resolution of 16 bits. Calculate the file size in KiB. Show your working.
Describe the effect of increasing the sample resolution on a sound file.
A recording uses 11 025 Hz and 8 bits. It is re-recorded at 22 050 Hz and 16 bits, with the same length. How many times larger is the new file? Explain.
A student says "changing the sample resolution from 8 bits to 16 bits gives twice as many amplitude levels." Explain why this is wrong.
Answer key and marking notes
- The sound wave is sampled.
- The amplitude (height) of the wave is measured at regular time intervals (set by the sample rate).
- Each measurement is stored as a binary number using a set number of bits (the sample resolution).
- Sample rate: the number of samples taken in a second.
- Sample resolution: the number of bits used to store each sample.
- 32 000 × 16 × 4 = 2 048 000 bits.
- 2 048 000 ÷ 8 = 256 000 bytes.
- 256 000 ÷ 1024 = 250 KiB.
- More amplitude levels can be represented, so the recording is more accurate (closer to the original sound).
- Each sample uses more bits, so the file size increases.
- The sample rate doubles, which doubles the size; the resolution doubles, which doubles it again.
- 2 × 2 = 4 times larger.
- 8 bits give 28 = 256 levels; 16 bits give 216 = 65 536 levels.
- That is 256 times as many levels (it is the file size that doubles).
6 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
What is meant by the sample rate of a sound recording?
- AThe number of samples taken in one second
- BThe number of bits used to store each sample
- CThe loudness of the sound when it is played back
- DThe total length of the recording in seconds
What is meant by the sample resolution of a sound recording?
- AThe number of bits used to store each sample
- BThe number of samples taken in one second
- CThe highest pitch the recording can contain
- DThe number of speakers used to play the sound
A recording studio increases the sample rate of a recording. What is the effect?
- AThe recording is more accurate and the file size increases
- BThe recording is more accurate and the file size decreases
- CThe recording is less accurate and the file size increases
- DThe accuracy is unchanged but the file size increases
A 10-second sound clip is recorded with a sample rate of 8000 Hz and a sample resolution of 8 bits. What is its file size in bytes?
- A80 000 bytes
- B640 000 bytes
- C8000 bytes
- D10 000 bytes
A 30-second sound clip has a sample rate of 16 000 Hz and a sample resolution of 16 bits. What is its file size in KiB?
- A937.5 KiB
- B960 KiB
- C7500 KiB
- D31.25 KiB
A recording's sample resolution is doubled from 8 bits to 16 bits, and at the same time its sample rate is halved. The length is unchanged. What happens to the file size?
- AIt stays the same
- BIt doubles
- CIt halves
- DIt becomes 4 times larger
Quiz key
The sample rate is how many times per second the amplitude of the sound wave is measured, in Hz. The number of bits per sample is the sample resolution. Loudness is the amplitude being measured, not the rate. The length in seconds is a separate value used in file size calculations.
Sample resolution is the number of bits per sample, so more bits allow more different amplitude levels to be stored. Samples per second is the sample rate. Pitch and speakers are not what the term describes.
Taking more samples each second follows the sound wave more closely, so the recording is closer to the original, and every extra sample must be stored, so the file is bigger. Accuracy never goes down when more samples are taken, and a file with more samples cannot be smaller.
8000 × 8 × 10 = 640 000 bits, and 640 000 ÷ 8 = 80 000 bytes. 640 000 is the size in bits, not bytes. 8000 bytes leaves out the 10 seconds. 10 000 bytes leaves out the 8-bit resolution.
16 000 × 16 × 30 = 7 680 000 bits; ÷ 8 = 960 000 bytes; ÷ 1024 = 937.5 KiB. 960 KiB divides by 1000 instead of 1024. 7500 KiB divides the bits by 1024 without first dividing by 8. 31.25 KiB leaves out the 30 seconds.
Doubling the resolution multiplies the size by 2 and halving the rate multiplies it by ½, so overall it is unchanged. Doubling or halving only looks at one of the two changes. 4 times larger would need both values to be doubled.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.