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Four Boxes in the Vocal Chain: Voltage or Numbers?

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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 chainAnalog chain (V)Digital chain (V)
At the microphone0.4370.437
After the converterno converter0.44
After the preamp0.4460.44
After the compressor0.4290.44
After the equalizer0.4520.44
After the reverb0.4210.44
1.
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.

2.
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.

3.
Which statement best describes the pattern in Table 1?
Question 3 options
4.
The boxes in the digital chain add noise to their pulses too. Why did the digital value stay the same after every box?
Question 4 options
5.
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 passedAnalog chain hissDigital chain hiss
121
241
361
481
6.
Use paragraph 4 and Table 2.

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

7.
Circle the two results that are evidence that noise builds up as an analog signal passes through more boxes.

8.
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?
Question 8 options
9.
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?
Question 9 options
10.
Sort each description by the chain it fits.
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.