Acoustics

• Sound is the perception of the vibration of our eardrums.
• The StdAudio is part of Sedgewick’s standard library that is used to play, manipulate, and synthesize sound.
• A musical note is a wave that oscillates at a certain frequency.
• StdAudio uses concert A, the A above middle C, as a reference note.
• Concert A (also known as A440, A4, Stuttgart pitch) has been standardized to oscillate at a frequency of 440 times per second (Hz).
• When you double or halve the frequency, you move up or down one octave on the scale. E.g., 880 Hz is one octave above concert A; 110 Hz is two octaves below concert A.

Acoustics, continued

• A newborn baby can hear sound waves of frequency between 20 to 20,000 Hz. People lose the ability to hear the high-frequency sounds as they grow older.
• The sin function repeats itself once every \(2\pi\) units, so if we measure \(t\) in seconds and plot \(\sin(2\pi t \times 440)\), we get a curve that oscillates 440 times per second.
• The amplitude of the wave determines what we perceive as volume. We'll plot our curves between –1.0 and +1.0 and assume the devices that record and play sound will scale as appropriate.
• When a guitar string is plugged, the string vibrates, producing a sine wave that is the prominent part of the sound that you hear and recognize as a note.
• There are 12 notes on the chromatic scale, evenly spaced on a (base 2) logarithmic scale. For any given note, we get the \(i\)th note above it by multiplying its frequency by \(2^{i/12}\).

Chromatic scale

Sampling

• For digital sound, we represent a curve by sampling it at regular intervals.
• We will use the commonly used sampling rate of 44,100 samples per second.
• For concert A, that rate corresponds to plotting each cycle of the sine wave by sampling it at about 100 points.
• We represent sound as an array of real numbers between –1.0 and +1.0.
• The play function of StdAudio takes a DoubleArray as its argument and plays the sound represented by that array on your computer.

StdAudio

• The StdAudio library has these functions
  • close(): Unit—closes standard audio
  • loop(filename: String): Unit—loops the audio file filename (in .wav, .mid, or .au format) in a background thread
  • play(sample: Double): Unit—plays sample for 1/44,100 second
  • play(samples: DoubleArray): Unit—plays the samples array
  • play(filename: String): Unit—plays the audio file filename (in .wav, .mid, or .au format) in a background thread
  • read(filename: String): DoubleArray—reads the audio samples from the file filename (in .wav or .au format) and returns them as a double array with values between -1.0 and +1.0
  • save(filename: String, samples: DoubleArray): Unit—saves samples to the audio file filename (using .wav or .au format).
• It also defines the Int constant SAMPLE_RATE to be 44100.

PlayThatTune

• Here is a simple-minded music player

  import kotlin.math.*
  import StdAudio.*
  fun main(args: Array<String>) {  
      val sc = java.util.Scanner(System.`in`)
      // Read a tune from standard input and play it.
      while (sc.hasNext()) {  
          // Read and play one note.
          val pitch = sc.nextInt()
          val duration = sc.nextDouble()
          val hz = 440 * 2.0.pow(pitch / 12.0)
          val n = (SAMPLE_RATE * duration).toInt()
          val a = DoubleArray(n+1) { sin(2*PI * it * hz / SAMPLE_RATE) }
          play(a)
      }
  }

• It reads lines from input of the form

  7 0.25
  6 0.25
  ...

  meaning the 7th note relative to concert A for 0.25 second; the 6th note relative to concert A for 0.25 second, etc, and successively plays them.