Lossy compression of a sound by reducing sample rate or sample resolution

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. A sound is lossy compressed by halving its sample rate. What happens to the file size?

A It gets smaller (about half)

B It stays the same

2. Which change is an example of lossy compression of a sound file?

A Increasing the sample rate from 22,050 Hz to 44,100 Hz

B Reducing the sample resolution from 16 bits to 8 bits

3. A sound is 4 MiB. After lossy compression by lowering the sample rate, it is 2 MiB. What was the quality loss?

A Temporary - the detail comes back when it is opened

B Permanent - the lost detail cannot be recovered

4. A sound file uses 16-bit sample resolution. It is reduced to 8 bits and nothing else changes. What is the new size compared with the original?

A Half the original size

B One quarter of the original size

5. To work out the saving after lossy compression of a sound, what should you do?

A Calculate the size before and after, then compare them

B Calculate the size once, using the new settings only

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1sample rate: 44100 Hz → 22050 Hz		ALossy compression permanently removes sound detail, so doubling the sample rate again cannot bring back the lost data
2sample resolution: 16 bits → 8 bits		B20000 / 2 × 16 × 60 = 10000 × 16 × 60 = 9600000 bits
3To find the size after halving the sample rate, recalculate with the new rate: rate × resolution × seconds		CFewer bits per sample means fewer total bits, so the file gets smaller, not bigger
4To show the saving from reducing 16 bits to 8 bits, compare the size before and after		Dbefore: 8000 × 16 × 10 = 1280000 bits, after: 8000 × 8 × 10 = 640000 bits
5Sample rate halved, so the original sound can be restored by doubling the rate again		EHalving the sample rate takes half as many samples each second, so the file size is halved and some sound detail is lost
6Reducing 16 bits to 8 bits makes the sound file bigger because the sound is simpler		FEach sample is stored with half as many bits, so the file size is halved but the sound is less accurate

Definitions

lossy sound compression

Fill in the Blanks

Complete each line of code by filling in the missing parts.

rate = 44100 newrate = rate / _

bits = 16 newbits = bits _ 2

rate = 44100 seconds = 10 sizebefore = rate * 16 * _______

sizeafter = newrate * 8 * seconds saving = sizebefore _ sizeafter

detaillost = True canrestore = _____

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A rate = 44100

B new_rate = rate * 2

C res = 16

D bits = new_rate * res * 10

Question 2

A rate = 8000

B res = 16

C new_res = 24

D new_bits = rate * new_res * 5

Question 3

A rate = 20000

B res = 8

C bits = rate + res * 30

D bytes = bits / 8

Question 4

A old_bits == 44100 * 16 * 10

B new_bits = 22050 * 16 * 10

C saved = old_bits - new_bits

Question 5

A old = 44100 * 16 * 10

B new = 22050 * 16 * 10

C saved = old - new

D saved_bytes = saved * 8

Answer Key

Lossy compression of a sound by reducing sample rate or sample resolution

Section A: Quick Questions

A — It gets smaller (about half)

B — Reducing the sample resolution from 16 bits to 8 bits

B — Permanent - the lost detail cannot be recovered

A — Half the original size

A — Calculate the size before and after, then compare them

Section B: Match the Pairs

sample rate: 44100 Hz → 22050 Hz → Halving the sample rate takes half as many samples each second, so the file size is halved and some sound detail is lost

sample resolution: 16 bits → 8 bits → Each sample is stored with half as many bits, so the file size is halved but the sound is less accurate

To find the size after halving the sample rate, recalculate with the new rate: rate × resolution × seconds → 20000 / 2 × 16 × 60 = 10000 × 16 × 60 = 9600000 bits

To show the saving from reducing 16 bits to 8 bits, compare the size before and after → before: 8000 × 16 × 10 = 1280000 bits, after: 8000 × 8 × 10 = 640000 bits

Sample rate halved, so the original sound can be restored by doubling the rate again → Lossy compression permanently removes sound detail, so doubling the sample rate again cannot bring back the lost data

Reducing 16 bits to 8 bits makes the sound file bigger because the sound is simpler → Fewer bits per sample means fewer total bits, so the file gets smaller, not bigger

Section C: Definitions

lossy sound compression — Lowering the sample rate or sample resolution of a sound so it needs fewer bits. The file gets smaller, but the lost sound detail can never be recovered.

Section D: Fill in the Blanks

rate = 44100
newrate = rate / 2

bits = 16
newbits = bits / 2

rate = 44100
seconds = 10
sizebefore = rate * 16 * seconds

sizeafter = newrate * 8 * seconds
saving = sizebefore - sizeafter

detaillost = True
canrestore = False

Section E: Spot the Error

B — Halving the sample rate means dividing by 2. Multiplying by 2 doubles the rate, which gives more data, not less. It should be new_rate = rate // 2.

C — Lossy compression lowers the sample resolution, for example from 16 bits to 8 bits. 24 bits is a higher resolution, so the file would grow. It should be new_res = 8.

C — File size in bits is sample rate x sample resolution x length in seconds. The rate and resolution must be multiplied, not added. It should be bits = rate * res * 30.

A — == compares two values, so nothing is stored in old_bits. Assigning the size before compression needs a single =. It should be old_bits = 44100 * 16 * 10.

D — The saving is in bits. To change bits into bytes you divide by 8, not multiply. It should be saved_bytes = saved / 8.