Sound Wave Lab

A recording is a series of measurements

A sound is a wave, and a wave is continuous. It has a value at every instant, and between any two instants there are infinitely many more. A computer cannot store that. It stores numbers, and however many it stores, it is a finite quantity. So it does the only thing available: it measures. At regular instants it takes a reading of the wave and stores that number, then waits a fixed interval and does it again. That is sampling, and what ends up in the file is the list of readings. ⚠️ Which means a digital recording is not a copy of a sound. It is a series of measurements of one, and no amount of care changes that. It is an approximation by construction. That single idea answers most of this topic. Quality is a question of how often you measured and how precisely each reading was stored. And unlike a photograph, a recording keeps taking measurements for as long as it runs - which turns out to matter enormously.

Words for digital sound

Five terms. The last three are the three numbers that decide the file size between them.

The same two dials, plus one

If you understood the image module, you already know two thirds of this. The third column is the part that is new.

How to size something measured over time

This calculation has one more stage than the one you did for images, and the extra stage is where nearly all the marks are lost. ⚠️ Count the measurements first, and remember that the count is itself a multiplication - how often, times how long. Skip that and you have sized one second of something that lasts a great deal longer. Then multiply by what each measurement costs, which gives you a total in bits. Then convert once, at the very end, to whatever unit was asked for - and say which convention you converted with, exactly as you did for images, because this specification accepts either and the same bits give two different figures. So: how many, times how much each, then convert once and name the basis. ⚠️ The commonest wrong answer on this topic is not a slip in the arithmetic. It is a correct calculation of the wrong thing, because the duration was left out.

Match each quantity to what it decides

Why sound files grow so fast

A photograph and a sound recording are both saved at good quality. The recording almost always ends up the larger file. Why?

• A picture has a fixed number of pixels, but a recording keeps producing samples for as long as it lasts, so the duration multiplies everything
• Each sound sample needs far more bits than each pixel of an image does
• Sound cannot be compressed, whereas images can be
• A recording has to store both the wave and a picture of it

One recording, all the way to kilobytes

A recording is made at a sample rate of 8,000 samples per second, a sample resolution of 8 bits, and it lasts 10 seconds. Work out the file size in kilobytes. How many measurements? 8,000 per second, for 10 seconds: 8,000 times 10 = 80,000 samples. ⚠️ This is the stage that has no equivalent in the image calculation, and the stage people miss. What does each cost? 8 bits. So 80,000 times 8 = 640,000 bits. In bytes: 640,000 divided by 8 = 80,000 bytes. In kilobytes: 80,000 divided by 1,000 = 80 kB, ⚠️ using the decimal convention, where one kilobyte is 1,000 bytes. Convert those same 640,000 bits using 1,024 instead and you get roughly 78.1 kB. Same recording, two correct figures, which is why the convention has to be stated - exactly as it did for images. ⚠️ Look at the shape of that working and compare it with the image one. They are the same calculation with one extra multiplication at the front. Count the entries, price the entries, convert once. The only new thing sound brings is that counting the entries takes two numbers instead of two dimensions.

How many measurements

A recording is made at a sample rate of 8,000 samples per second and lasts 5 seconds. Work out how many samples are taken altogether.

Total bits in the recording

A recording contains 20,000 samples, and each sample is stored using a sample resolution of 4 bits. Work out the total size of the recording in bits.

Order the sound size calculation

Put the steps of working out a sound file size into the order you should carry them out.

• Multiply the sample rate by the duration to find how many samples there are
• Multiply that by the sample resolution to find the size in bits
• Divide by eight to express the same size in bytes
• Convert once more to reach the unit the question asked for
• State which convention was used for that conversion

Complete the digital sound paragraph

Measuring a continuous wave at regular instants and storing each measurement is called _____. The number of those measurements taken every second is the _____. The number of bits each individual one is stored in is the _____. How long the whole recording lasts is its _____.

True about digital recordings

Select the TWO statements that are true.

• Raising the sample rate takes more measurements each second, so the file grows
• A digital recording is an approximation of the original wave rather than an exact copy
• Raising the sample resolution takes more measurements each second
• A longer recording made at the same settings comes to the same file size

Spot the true digital sound facts

Tap the TWO statements that are true.

• Sample resolution is the number of bits used for each sample
• Doubling the duration doubles the file size, with everything else unchanged
• Sample rate is the number of bits used for each sample
• A digital recording captures the original wave exactly

Three recording calls

Three situations. Choose the answer that gives the reason as well as the decision.

• A recording is too large to upload. It has to stay the same length and keep the same sample rate. What can be changed?
• A student calculates a sound file size, multiplies the sample rate by the sample resolution, and stops there. What have they actually worked out?
• A student finishes the calculation and writes the answer as "80", with nothing else. What is missing?

Explain how sound is stored and sized

A friend has learned the image file-size calculation and assumes sound works the same way. Write them the answer that shows what carries over and what does not.

• Explain what sampling is, and why a digital recording can never be an exact copy of the original wave
• Explain what the sample rate and the sample resolution each control
• Explain what sound has that a still image does not, and why it matters so much to the file size
• Show how to calculate the size of a recording, setting out every stage of the working
• Finish by saying when to convert to the unit asked for, and what else must be stated alongside the number