Companion to the reading passage Sound Waves & Active Noise Cancellation. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
On a long flight, the steady drone of the jet engines fills the cabin. Active noise-cancelling (ANC) headphones reduce this noise by adding more sound. Sound is a longitudinal wave: a pattern of compressions (higher air pressure) and rarefactions (lower air pressure) moving through the air. A small microphone on each ear cup detects the incoming noise. A processor then drives a speaker inside the ear cup to produce an “anti-noise” wave. Where the two waves overlap at the ear, they superpose, and the combined pressure variation can be much smaller than the noise alone.
Model 1: A graph of air-pressure change versus time shows the engine hum at the listener’s ear. The wave is a smooth sine curve with an amplitude of 0.20 Pa and a frequency of 120 Hz. It starts at 0 Pa at t = 0 ms, rises to +0.20 Pa at t = 2.1 ms, returns to 0 Pa at 4.2 ms, falls to −0.20 Pa at 6.3 ms, and returns to 0 Pa at 8.3 ms. Sound travels through the cabin air at 343 m/s.
Model 1: Engine Hum at the Ear (one cycle, 0–8.3 ms)
1. Which graph shows one cycle (0 ms to 8.3 ms) of the anti-noise pressure wave that the speaker must produce to cancel the engine hum in Model 1 as completely as possible?
2. Substitute numerical values into a mathematical representation that can be used to determine the wavelength of the engine hum in the cabin air. Then calculate the wavelength.
Engineers tested a pair of ANC headphones on a model head with a microphone inside each ear. They played four recorded sounds and measured the sound level at the ear, first with ANC turned off and then with ANC turned on. The difference between the two readings is the noise reduction, measured in decibels (dB). On the decibel scale, each decrease of 10 dB means the sound intensity has decreased to one-tenth of its earlier value. The results are shown in Table 1.
Data are representative values for practice.
Table 1: Noise Reduction with ANC Turned On
| Sound Source | Frequency (Hz) | Behavior of Sound | Noise Reduction (dB) |
|---|---|---|---|
| A: Jet engine hum | 120 | steady, constant | 15 |
| B: Air-conditioner fan | 250 | steady, constant | 14 |
| C: Sudden siren | 2,500 | sudden, unpredictable | 2 |
| D: Crying infant | 1,000–3,000 | rapidly changing pitch | 3 |
3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response with evidence from the passage and Table 1.
4. Which statement best describes the pattern in the data in Table 1?
The anti-noise wave is useful only if it reaches the ear at the right moment. Together, the microphone, processor, and speaker delay the anti-noise wave by about 0.10 ms. Engineers could shorten this delay with faster processors, but faster processors drain the battery more quickly. Instead, most designs combine ANC with padded ear cups, which block high-frequency sounds well but block low-frequency sounds poorly.
5. Which mathematical representation can be used to determine the period of the siren sound, Source C?
6. Using the 0.10-ms delay, explain why the anti-noise wave can effectively cancel the 120-Hz engine hum but cannot effectively cancel the 2,500-Hz siren.