Practice Exam Answer Key

Practice exam answer key.

1A. It is a not a piccolo because the fundamental is at about 70 Hz and so this is a low note. It is not a drum because the spectrum is harmonic, also there is no flat spectrum component. It could either be a low note on the piano or a didgeridu. However there is a peak in the overtone strengths at about 1kHz that is similar to a format so the sound is probably from a digi not a piano.

1B. The sixth overtone is at 400 Hz. This means the fundamental is at about 66.67Hz. I multiply this by 4 to get 2 octaves higher finding 266.7Hz so I can compare to the list of frequencies of notes for the tempered scale. This is in between a C4 and C#4, but closer to a C4. Since my note was two octaves lower it is about a C2.

2a. The horizontal lines in a ladder shape (integer harmonics of a fundamental frequency) correspond to notes played by the flute. Vertical lines are percussive as they don’t have strong spectral components. There are also tones associated with the drums as the drum heads oscillate at particular frequencies. The wiggles at the bottom (at about 100Hz) are tones from the large tabla. Vertical bars without the low wiggles are from the smaller tabla.

2b. At time 16.4s the third harmonic is at about 2000Hz. So the fundamental is at about 666.7Hz. Divide this by 2 finding 333Hz so we can compare to the notes in the tempered scale. This is closest to E4. So the highest note is about an E5.

3) It is not a piccolo or a harp as both would have tones in the spectrum and this has a nearly flat spectrum (or power at all frequencies). The spectrum could be that of a percussive onset like a clap however the waveform view shows that the sound stays at the same volume for a long time. Sounds with constant volume and smooth spectra are often called noise. This one has a nearly flat spectrum so we would call it “white” noise.

4) The spectrum it typical of something with a fundamental and overtones that are integer multiples of the fundamental. The fundamental is decreasing in frequency with time so the scale is going downwards in pitch. The waveform view does not show a sharpdecay or drop in volume typical of a plucked string. Hence this is probably a piccolo. The highest note played is at about 1500Hz and this is high (divide by 4 to get 375Hz in the 4th octave which is an F#4 or so). The first note played is actually a G6 and this is high, as would be expected for a piccolo.

5. a) It is a digi. Why? It is low with fundamental like 70 Hz. To guess more accurately we take the 15th harmonic at 1000Hz and divide by 15 to get 67Hz.

Note that the odd integer harmonics seem or louder (particularly at the bottom) than some of the even harmonics. This might be characteristic of this digi and would not be typical of a bass singer or an electric bass.

b) 67Hz times 4 gives you 268Hz which is close to C4. The note played is then close to a C2.

c) The spectral variations are similar to formats and are made by moving the mouth when blowing. A singer could have a similar spectrum but would not be restricted to a single pitch.

d) You can see wiggles in the higher frequency overtones. The pitch is higher when the notes are louder. When the players blows harder there tends to be a somewhat higher pitch and stronger higher overtones.

e) Odd integer overtones might be weaker because the instrument behaves like a pipe that is closed at one end. On the other than digis are typically flared and so the spectrum is not exactly that of a simple cylinder. Because the lips and close at the same frequency as one of the modes of the pipe, the spectrum is harmonic however some of the overtones may be damped because these frequencies are not well excited in the pipe. When the mouth is moved some of the higher overtones are damped or exited more than others. This causes variations in the strengths of the overtones, as occurs in speech with formats.

f) Because the lips open and close at the same frequency as one of the modes of the pipe and in a periodic pattern. Because the motion is nearly periodic, the entire pattern is nearly harmonic.

6)a) This is a singer. We can tell because the spectrum shows formats or bands of overtones that are brighter than other bands. It’s not a digi as different pitches ore notes are seen (or played) and there are large pitch variations even in a single note. The waveform view is odd because the singer is singing “bahm” and the initial “b” gives a loud sound at the beginning of each note. The envelope seen in waveform view implies that the instrument is not plucked or hit (though I suppose a bowed instrument could look similar). A blown instrument does not usually have formants.

b) Pitch variation depends on the stiffness of the vocal chords. Strengths of the overtones are affected by the position of throat and mouth.

c) Vocal chords open and close at a particular frequency. The motion is nearly periodic but not a sine wave. Because the waveform is nearly periodic the spectrum is harmonic (and overtones are integer multiples of a fundamental).

7 A. A percussive onset is seen (flat or smooth spectrum). The waveform view shows a rapid decay. The instrument is either plucked or hit as the decay is fast. Overtones are not integer multiples of a fundamentalfrequency so the instrument is not voice, a wind instrument or a stringed instrument. The instrument is most likely something percussive. Percussion instruments such as bells often have overtones that are not integer multiples of a fundamental.

B. Because of its non-harmonic spectrum it can’t be a harp or a flute. We can see that the pitch changes each time the instrument is hit so it can’t be a single drum. It must be bamboo tubes of different lengths.

8) This one is very similar to 7 and must be copper pipes. The notes are going down.

9. A. The third harmonic is free. This harmonic motion has 2 nodes and the note is an octave and a fifth above the fundamental. The finger probably touches the string 1/3 of the length down from one of the ends.

B. If the original note is an A2, the second harmonic would be an A3 and the third an E4.

C. Only harmonics with nodes at 1/3 the length of the string can sound after the string is touched. The other modes would move at this spot and so are damped. The sixth harmonic can ring and the ninth, etc.

10. a) the note starts high then drops then goes high again.

b. The highest note has a fundamental at about 1700Hz. This is at about the 5th harmonic of the lowest note. So the interval is about 2 octaves and a third. The frequency ratio is about a factor of 5.

c,d) It is a sliding whistle and odd harmonics are likely weaker than the even ones because one end is closed.

11. Looking at the first 6 peaks: The first, third, firth and sixth appear to be an equally spaced set. The second, fourth and sixth peaks seem to be an equally spaced set. The sixth peak is probably an overtone for both sets and it is at about 1050Hz.

Divide this by 3 and we get 350Hz (about F4). Divide 1050Hz by 4 and we get 262Hz (C4). The ratio between these two is 4/3 so the interval is probably a fourth. And this ratio 4:3 is consistent with 1050Hz being the fourth harmonic for one note and the third harmonic for the other. All other peaks are fairly straightforward to identify from this pattern.

12. a) About ¼ of the way into the clip the sopranos come in.

b) The lowest note is the first note and the fifth harmonic is about 0.5kHz or 500Hz. Divide by 5 and we get a fundamental of about 100Hz. Multiply by 3 and look at the table showing the tempered scale. 300Hz is about a D4. Since we are two octaves lower, we would estimate a D2.

13. The third harmonic of one note matches the second of the other. The ratio is 3/2, the interval a fifth.