Four Boxes in the Vocal Chain: Voltage or Numbers?

Follow one instant of a voice through an analog and a digital studio chain.

Part 1: One instant of a voice

Read the studio notes and Table 1. Then answer questions 1 to 5.

One Voice, Four Boxes

1The Harbor Lane Community Music Studio lets teens record their own songs on weekends. Eighth grader Elan Prescott is recording a vocal track with the studio's sound engineer, Ms. Sabine Okonjo. A microphone turns the sound wave of Elan's voice into an electric signal, a voltage that rises and falls in step with the wave. Before the signal reaches the recorder, it passes through four boxes: a preamp that makes it stronger, a compressor that evens out loud and soft parts, an equalizer that adjusts high and low pitches, and a reverb unit that adds an echo like a large hall.

2The studio can connect the boxes in two ways. In the analog chain, each box works on the smooth voltage itself, and cables carry that voltage from box to box. Every box and cable adds a tiny amount of noise, small random changes in the voltage that are heard as hiss. In the digital chain, a converter right after the microphone digitizes the signal. It measures the voltage 48,000 times each second and rounds each measurement to the nearest 0.01 V. Each rounded measurement is stored as a number and sent from box to box as a pattern of on and off pulses. The boxes change the numbers by calculation, and each box only has to decide whether each pulse it receives is on or off.

3To compare the two chains, Ms. Okonjo followed a single measurement. At one instant of Elan's voice, a meter at the microphone read 0.437 V. For this test she set every box to pass the signal along without changing it on purpose, so any change in the value came from noise or from rounding. Table 1 shows the value at that instant after each step in both chains.

4Next, Elan stood silently in the vocal booth while each chain recorded 10 seconds with every box switched on. Ms. Okonjo measured the hiss in the silent recording on the studio's meter, where 0 means no sound at all. She plugged the recorder in after one, two, three and then all four boxes. Table 2 shows her readings. Listeners in the studio usually hear hiss when the meter reads 5 or more.

Table 1: One Instant of Elan's Voice
Point in the chain	Analog chain (V)	Digital chain (V)
At the microphone	0.437	0.437
After the converter	no converter	0.44
After the preamp	0.446	0.44
After the compressor	0.429	0.44
After the equalizer	0.452	0.44
After the reverb	0.421	0.44

Use paragraph 2 and Table 1. The converter rounded 0.437 V to the nearest 0.01 V.

The rounding changed the value by V.

Use Table 1. Compare the analog value after the reverb with the value at the microphone.

After all four boxes, the analog value was off by V.

Which statement best describes the pattern in Table 1?

A. The analog value went up at each box, so the voice got a little louder in that chain.
B. The digital value moved farther from 0.437 V at each box, while the analog value held steady.
C. The analog value wandered farther from 0.437 V, while the digital value stayed at 0.44 V.
D. Both chains were off by about the same amount after the reverb, so neither chain did better.

The boxes in the digital chain add noise to their pulses too. Why did the digital value stay the same after every box?

A. Small noise did not change whether a pulse read as on or off, so the number arrived unchanged.
B. The converter rounded away the noise from each box as the signal traveled through the chain.
C. The digital boxes were made with quieter parts, so they added far less noise to the voltage itself.
D. The pulses moved through the cables faster, so the noise had less time to build up on them.

Use paragraph 2. The converter always rounds to the nearest 0.01 V. Think about a measurement that falls exactly halfway between two steps.

Rounding can change any measurement by at most V.

Part 2: Hiss in a silent recording

Use paragraphs 2 and 4, Table 2 and what you found in Part 1.

Table 2: Hiss in 10 Seconds of Silence (studio meter, 0 = no sound)
Boxes the signal passed	Analog chain hiss	Digital chain hiss
1	2	1
2	4	1
3	6	1
4	8	1

Use paragraph 4 and Table 2.

Listeners would first hear the hiss in the analog chain once the signal had passed through boxes.

Circle the two results that are evidence that noise builds up as an analog signal passes through more boxes.

The analog hiss rose from 2 after one box to 8 after four boxes.The digital hiss read 1 after every number of boxes.The analog value was 0.009 V off after one box and 0.016 V off after all four boxes.The converter stored the 0.437 V measurement as 0.44 V.Both chains started from the same microphone reading of 0.437 V.

Suppose Ms. Okonjo adds a fifth box, a delay unit, to the end of each chain and records silence again. Based on Table 2, what is the most likely result?

A. Analog hiss near 6 and digital hiss near 1, since the hiss settles down after four boxes
B. Analog hiss near 10 and digital hiss near 3, since each new box adds about 2 to both chains
C. Analog hiss near 8 and digital hiss near 3, since the digital hiss catches up with more boxes
D. Analog hiss near 10 and digital hiss near 1, since only analog hiss grows with each box

To save storage space, a student suggests rounding to the nearest 0.1 V instead of 0.01 V. The 0.437 V measurement would then be stored as 0.4 V. Which result is most likely?

A. The voice would be stored just as exactly, since each pulse is still read as on or off.
B. Each number could be up to 0.05 V off, but the boxes would still pass it along unchanged.
C. The boxes would now change the stored numbers, so the digital hiss would grow at each box.
D. The stored numbers would drift a little farther from 0.4 V after each box, like the analog values.

10.

Sort each description by the chain it fits.

Each box works on the smooth voltage from the microphone.A box only has to decide whether each pulse is on or off.The value of one instant stayed at 0.44 V after the reverb.The hiss in a silent recording rose by about 2 with each box.A small, fixed error is made once, when the voltage is rounded to a step.

Analog chain	Digital chain

11.

A band member says, "The analog chain is more accurate. The digital chain rounds every measurement, so it changes the voice before it even starts." Do you agree? Write a claim, give evidence from both tables, and explain your reasoning about how noise affects analog and digitized signals.