Range of hearing

The audible range is a window on the frequency axis. A healthy young human ear responds to sound waves whose frequency $f$ satisfies

where: $f$ is the frequency of the sound wave in hertz (Hz), the lower bound $20\ \text{Hz}$ is the smallest frequency the ear can turn into a nerve signal, and the upper bound $20{,}000\ \text{Hz} = 20\ \text{kHz}$ is the largest. Any wave with $f$ inside this band is, by definition, audible; anything outside it is not — regardless of how loud (large-amplitude) the vibration producing it is. Loudness and frequency are independent properties of a wave, and only frequency decides whether the ear's mechanism can respond at all.

Two named zones lie outside the window. Sound below the lower bound is called infrasonic sound (infrasound): $f < 20\ \text{Hz}$. Sound above the upper bound is called ultrasonic sound (ultrasound): $f > 20{,}000\ \text{Hz}$. Both obey exactly the same wave physics as audible sound — they travel, reflect, and carry energy the same way — the only thing that changes is whether the human ear's internal structures can convert that particular frequency into a signal the brain interprets as sound.

Nature exploits both zones. Elephants, whales, and rhinoceroses produce and sense infrasonic rumbles to communicate over very long distances, and the low-frequency tremors before an earthquake are also infrasonic. Bats and dolphins produce and detect ultrasonic clicks to navigate and hunt by echo, and a dog's upper hearing limit reaches well above a human's, which is why a dog whistle (tuned into the ultrasonic zone) is silent to us but sharp to a dog.

The window shifts slightly with the individual. The figures 20 Hz to 20 kHz describe a typical healthy young adult; the upper limit tends to fall somewhat with age, and sensitivity differs from person to person. This is the standard reference range used throughout Class 9 Physics, and it is the range you should quote unless a question specifies otherwise.

A brief note on the path sound takes. Once a wave with a frequency inside the audible window reaches the ear, the outer ear funnels it toward the eardrum, which vibrates in step with the wave; that vibration is passed on through the middle and inner ear and eventually converted into nerve impulses the brain reads as sound. The detailed anatomy of this pathway belongs to Biology, not this Physics chapter — here it is enough to know that the eardrum is the first structure that must respond, and it is precisely this structure's mechanical limits that create the 20 Hz to 20,000 Hz window in the first place.

This topic has no formula to derive; its physics is a definition plus a comparison, so the useful skill is understanding why the boundary exists and how to apply it, rather than deriving a number.

The boundary is set by the ear, not by the wave. A sound wave of, say, 10 Hz is a perfectly ordinary pressure vibration travelling through air, obeying the same wave equations as a 1,000 Hz wave. What differs is the human ear: its eardrum and inner-ear structures are mechanically tuned to respond efficiently only within roughly 20 Hz to 20,000 Hz. Below 20 Hz the vibrations are too slow for the ear's mechanism to generate a continuous nerve signal the brain reads as a tone; above 20,000 Hz they are too fast for the same structures to follow. So "audible" is a statement about a detector's limits, not a statement about which frequencies are "real" sound.

Classification is a single comparison, always in this order. Given a frequency $f$, first check $f < 20\ \text{Hz}$ (infrasonic); if not, check $f > 20{,}000\ \text{Hz}$ (ultrasonic); if neither, $f$ lies in the audible range. This three-way test is the entire method — no calculation beyond comparing two numbers.

Different animals carry different detectors. Because the boundary belongs to the ear and not the wave, an animal with a different-tuned ear hears a different window of the same universal set of frequencies. Dogs, bats, and dolphins have hearing that extends further into the ultrasonic zone than humans; elephants and whales are especially sensitive at the low, infrasonic end. This is exactly why the same 25,000 Hz whistle can be silent to a person and startling to a dog standing beside them — the wave reaching both ears is identical, only the detectors differ.

A wildlife recorder captures three signals: 15 Hz from a distant elephant herd, 5,000 Hz from birdsong, and 40,000 Hz from a bat's echolocation call. Classify each signal and state which of the three a human researcher standing nearby could actually hear.

Step 1. Recall the audible window: $20\ \text{Hz} \le f \le 20{,}000\ \text{Hz}$; below it is infrasonic, above it is ultrasonic.

Step 2. Classify the elephant signal. Since $15\ \text{Hz} < 20\ \text{Hz}$, this is infrasonic sound; it lies outside the audible range on the low side.

Step 3. Classify the birdsong signal. Since $20\ \text{Hz} \le 5{,}000\ \text{Hz} \le 20{,}000\ \text{Hz}$, this frequency lies inside the audible range — it is a normal audible sound.

Step 4. Classify the bat signal. Since $40{,}000\ \text{Hz} > 20{,}000\ \text{Hz}$, this is ultrasonic sound; it lies outside the audible range on the high side.

Answer: The elephant infrasound (15 Hz) and the bat ultrasound (40,000 Hz) would both be inaudible to the researcher; only the 5,000 Hz birdsong falls inside the human audible range and would actually be heard.

• Mixing up units. $20{,}000\ \text{Hz}$ and $20\ \text{kHz}$ are the same number; a misplaced zero turns 20,000 Hz into 2,000 Hz (which is well inside the audible range) and gives a wrong classification.
• Assuming infrasonic and ultrasonic sounds are not "real" because humans cannot hear them. Both are genuine sound waves following the same physics as audible sound; only detectability by the human ear differs.
• Confusing ultrasonic with loud. Ultrasonic describes frequency above 20,000 Hz, not intensity; an ultrasonic wave can be faint, and an audible wave can be deafening — loudness and frequency are separate properties.
• Treating 20 Hz to 20,000 Hz as a fixed, universal number for every person. It is the typical figure for a healthy young adult; the upper limit generally decreases with age, and it is used as the standard reference in this chapter.

Ask the tutor: Curious how bats use ultrasound to hunt in total darkness, or want to practice classifying a batch of frequencies quickly — ask the AI tutor to walk through it with you.