Which of the following are true about sound? (A) 10 decibel (dB) increase in…

CONCEPT

The decibel is a logarithmic ratio measure of sound, not a linear one. The sound level L of an intensity I, referred to a reference intensity I0, is defined as L = 10 log10(I/I0). Because the scale is logarithmic, ADDING a fixed number of decibels MULTIPLIES the intensity by a fixed factor: a level change of ΔL decibels corresponds to an intensity ratio of 10ΔL/10. Every 10 dB therefore contributes one full power of ten.

Two further definitions govern the remaining ideas. Intensity is the physical acoustic power carried per unit area, an objectively measurable quantity; loudness is the subjective auditory sensation the ear and brain form in response to it, which is why equally intense tones at different frequencies are not heard as equally loud. And the frequency band an average human ear responds to runs from about 20 Hz to about 20 kHz; outside it the Latin prefixes name the two sides — infra- means below, so vibrations under 20 Hz are infrasound, and ultra- means beyond, so vibrations above 20 kHz are ultrasound.

APPLICATION

Each of the five statements is measured against those definitions in turn:

1. The 10 dB claim: substituting ΔL = 10 into the ratio rule gives 1010/10 = 101 = 10, so a 10 dB rise multiplies the intensity by ten. A tenfold description of a 10 dB rise is exact.

2. The 20 dB claim: substituting ΔL = 20 gives 1020/10 = 102 = 100, so a 20 dB rise multiplies the intensity by one hundred. A twentyfold description of a 20 dB rise is off by a factor of five, and it is the classic error of reading a logarithmic scale as if it were linear.

3. The loudness claim: intensity is what an instrument measures, loudness is what a listener experiences from it. Describing loudness as the human perception of sound intensity is the standard definition of the term.

4. The audible-range claim: the conventional band of human hearing is quoted as 20 Hz to 20 kHz, which is exactly the interval stated.

5. The naming claim: by the prefix rule above, below 20 Hz is infrasound and above 20 kHz is ultrasound. A statement that calls sub-20 Hz sound ultrasound and above-20 kHz sound infrasound has the two names interchanged.

CROSS-CHECK

The decibel rule can be re-checked from the other direction: since each 10 dB adds one power of ten, the ladder runs 10 dB → 10×, 20 dB → 100×, 30 dB → 1000×. Conversely, a genuine twentyfold rise in intensity is 10 log10 20 ≈ 13 dB, not 20 dB. The decibel count and the intensity multiplier are different quantities; among the ladder steps just listed they read as the same number only at 10 dB. The prefix rule can be checked against light, where the same Latin pair is used the same way: infrared lies below red in frequency and ultraviolet beyond violet.

The statements that survive both checks are the 10 dB tenfold-intensity statement, the loudness-as-perception statement and the 20 Hz to 20 kHz audible-range statement — the grouping "(A), (C) and (D) Only".