Unit of loudness

Loudness is how strong or weak a sound feels to a listener. You already know the starting fact from earlier in this chapter: loudness increases when the amplitude of the vibrating source increases. A guitar string plucked hard swings through a bigger amplitude than one plucked gently, and it sounds louder. But amplitude is not the whole story, and this is precisely what makes loudness different from frequency. Frequency depends on exactly one thing — how fast the source vibrates — so it has one clean formula, $f = 1/T$, and one clean unit, the hertz. Loudness depends on at least three things at once, and none of them alone fixes it:

• Amplitude of vibration at the source. This is the main physical driver — a bigger amplitude means the source carries more sound energy outward, so, all else equal, the sound feels louder.
• Distance from the source. Sound energy spreads outward as it travels, so it gets weaker the further it goes. The same source sounds loud up close and faint from across a field, even though nothing about the source itself has changed.
• Sensitivity of the listener's ear. Human ears are not identical detectors. Two people standing at exactly the same spot, hearing exactly the same sound, can judge it differently loud, because ear sensitivity varies from person to person (and even changes with age or hearing health).

Because loudness mixes a physical cause — energy carried by the vibration — with distance and a subjective judgement by the ear, it cannot be pinned to a single simple number the way frequency can. Scientists therefore built a special scale to compare loudness in a standard way: the decibel, written dB. You are not expected to calculate with decibels at this stage, or to know the formula behind the scale — that arrives in later classes alongside sound intensity. For now you only need to recognise dB as the name of the unit used to state and compare how loud everyday sounds are: a whisper sits around 20 to 30 dB, ordinary conversation around 60 dB, and a jet engine can exceed 120 dB — numbers you might see quoted on a sound-level meter, without needing to compute a single one of them yourself.

where: this is not a formula to substitute into — it is a reminder that loudness is jointly decided by three separate factors, unlike frequency ($f = 1/T$), which is decided by one.

Loudness resists a single formula because energy, geometry and biology all act on it together, and each acts independently of the others. Start with energy. A vibrating source pushes on the air around it, and a larger amplitude means the source is doing more work on the air with each vibration, so it radiates more sound energy per second. More energy reaching the ear generally produces a stronger sensation — this is the amplitude link you already know. Now bring in geometry. Once sound leaves the source, it spreads outward through the air in all directions, like ripples widening on a pond. The same total energy has to cover an ever-larger area the further it travels, so the energy reaching any one listener's ear falls off with distance. This is why identical amplitude at the source can feel loud to a nearby listener and faint to a distant one — nothing about the vibration changed, only the distance the energy had to spread across. Finally, biology intervenes. The ear does not passively record incoming energy the way a simple meter would; it is a biological detector whose sensitivity differs from person to person, and even changes with the frequency of the sound and the health of the listener's hearing. So the very last step — turning received sound energy into a felt sensation of "loud" or "soft" — is not fixed by physics alone. Put these three together and you see why no single clean formula like $f = 1/T$ can capture loudness: it would need to account for the source's energy, the geometry of spreading, and a variable human detector, all at once. That is exactly why the decibel scale exists — not as a formula students calculate, but as a standard, agreed way to state and compare loudness values, built by scientists who studied all three factors carefully, even though the details of that scale belong to later classes.

A siren is sounded at a fixed volume. Priya stands close to the siren; her friend Devansh stands much further away in an open field, and both have normal hearing. Later, the siren's volume is turned up (so its amplitude increases) while Priya and Devansh stay exactly where they were. Explain, step by step, (a) why Priya and Devansh disagree about the loudness even before the volume changes, and (b) what happens to each of their experiences after the volume is increased.

Step 1: Identify the factor separating Priya and Devansh before any change. The siren's amplitude and frequency are the same for both listeners — only their distance from the source differs. Priya, being closer, receives more of the siren's spreading sound energy than Devansh.

Step 2: State the result before the volume change. Priya perceives the siren as louder than Devansh does, purely because of distance, even though the source itself is identical for both of them.

Step 3: Identify what changes when the volume is turned up. Turning up the volume increases the amplitude of the siren's vibrating diaphragm. A larger amplitude means the source now radiates more sound energy outward than before.

Step 4: Apply the increased amplitude to both listeners. Since both Priya and Devansh remain at their original distances, the extra energy from the larger amplitude reaches both of them, so both should now perceive a louder sound than before the volume was raised.

Step 5: Conclude. Priya still sounds louder than Devansh at every stage, because distance has not changed — but after the volume increase, both of them independently perceive a louder siren than they did before, because amplitude at the source has increased for both. Distance explains the gap between Priya and Devansh; amplitude explains the change over time for each of them.

• Trying to calculate loudness in decibels using a formula. At this level, you only need to know the decibel (dB) by name as the unit used to compare loudness — no calculation is expected of you.
• Treating loudness as caused by one single factor. Frequency depends only on the rate of vibration, but loudness depends jointly on amplitude, distance, and the listener's ear sensitivity — leaving any one out gives an incomplete explanation.
• Confusing loudness with amplitude. Amplitude is a fixed physical property of the vibrating source at a given instant; loudness is the sensation it produces in a listener, which also depends on how far that listener stands and how sensitive their ear is.
• Assuming a sound needs a decibel number to be described as loud or soft. "Loud" and "soft" are valid qualitative descriptions tied directly to amplitude and distance, even with no decibel value stated.

Ask the tutor: Curious how a sound-level meter actually turns sound energy into a decibel number, or want to explore how loudness and pitch are measured together in real instruments? Ask your AI tutor to walk through it with you.