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Answers

F8.8 Sound

Data representation · GCSE · OCR J277 1.2.4, AQA 8525 3.3.7, Edexcel 1CP2 2.2.3 · about 15 min

BugBotLab

What this lesson is about

Sampling, sample rate, bit depth and file size, and finding a note from its samples.

Questions 5 marks in all

  1. [1 mark]A sound is sampled at 8,000 Hz with an 8-bit depth for 2 seconds. How many bits is it?

    Answer: 128000. 8,000 × 8 × 2.

  2. [1 mark]What is the sample rate?

    1. AThe number of samples taken each second
    2. BThe number of bits in each sample
    3. CHow loud the sound is
    4. DThe length of the recording
    Answer: A. Measured in hertz: samples per second.

  3. [1 mark]What does increasing the bit depth do?

    1. AEach sample is stored more accurately, and the file gets bigger
    2. BMore samples are taken each second
    3. CThe sound gets louder
    4. DThe file gets smaller
    Answer: A. More bits give more levels for each measurement.

  4. [1 mark]A 440 Hz wave crosses the middle going upwards how many times in half a second?

    Answer: 220. Once per cycle: 440 × 0.5.

  5. [1 mark]How many levels can a 2-bit sample take?

    Answer: 4. 2 to the power 2.

The task: find the note

Sample a note of 659 Hz for half a second at a sample rate of 8,000 Hz. Print samples: <n> and 8-bit size: <n> bits, worked out from the rate and duration. Then count the upward crossings, print note: <freq> Hz, and play that frequency on the buzzer for half a second.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

import math

rate = 8000
seconds = 0.5

The hint students can ask for: Build the samples with a sine wave, then find the frequency by counting how many times the wave crosses zero on the way up. Divide those crossings by how long the recording lasted.

A solution

from bugbot import *
connect()
import math

rate = 8000
seconds = 0.5
samples = [math.sin(2 * math.pi * 659 * i / rate) for i in range(int(rate * seconds))]
print("samples:", len(samples))
print("8-bit size:", len(samples) * 8, "bits")
rises = 0
for i in range(1, len(samples)):
    if samples[i - 1] < 0 <= samples[i]:
        rises = rises + 1
freq = round(rises / seconds)
print("note:", freq, "Hz")
tone(freq, 0.5)

Any program that meets the task's checks is marked correct in the simulator; this is one way, not the only way.