State the approximate range of frequencies audible to humans as 20 Hz to 20000 Hz

Topic 3.4 – Sound

Learning Objectives

• State the approximate range of frequencies audible to a typical healthy human ear: ≈ 20 Hz – 20 kHz.
• Explain how a vibrating source produces sound by successive compressions and rarefactions.
• Describe the longitudinal nature of sound waves and why a material medium is required.
• Recall the approximate speed of sound in air (≈ 330 – 350 m s⁻¹) and how it varies with temperature and with the medium.
• Outline a simple classroom method for measuring the speed of sound and note relevant safety precautions.
• Distinguish the effects of frequency on pitch and of amplitude on loudness, including a quantitative example.
• Define the terms *infrasound* and *ultrasound* and state the frequency limits that separate these regions.

What Is Sound?

Sound is a **mechanical longitudinal wave** that propagates through a material medium (solid, liquid or gas) by successive compressions and rarefactions of the particles of that medium.

How Is Sound Produced?

• A solid object (e.g., a tuning‑fork, a speaker diaphragm, a guitar string) is set into vibration.
• Each vibration pushes the adjacent particles of the surrounding medium together (compression). Those particles then push the next layer, and the process repeats, creating a chain of particle‑collision events.
• The alternating high‑pressure (compression) and low‑pressure (rarefaction) regions travel away from the source as a sound wave.

Longitudinal Nature of Sound Waves

In a longitudinal wave the particle displacement is **parallel to the direction of wave travel**. The diagram below (suggested) shows a snapshot of compressions and rarefactions moving along the x‑axis.

Why a Material Medium Is Needed

• Sound is a mechanical disturbance; it requires particles to transmit the pressure variations from one region to the next.
• In a vacuum there are no particles, so no sound can travel.
• By contrast, electromagnetic waves (e.g., light) are not mechanical and can propagate through a vacuum.

Speed of Sound

• In dry air at 20 °C, the speed is ≈ 343 m s⁻¹. The syllabus expects the approximate range 330 – 350 m s⁻¹, which should be stated explicitly.
• The speed increases with temperature at roughly **0.6 m s⁻¹ per °C**.
• It is higher in liquids and solids because the particles are much closer together, allowing pressure variations to be transmitted more rapidly.

Classroom Method – Echo Technique

1. Place a loudspeaker a known distance d from a flat, hard wall (a flat surface gives a clear echo).
2. Produce a short, sharp sound (e.g., a hand‑clap or a burst from the speaker) and use a microphone linked to a stopwatch or a computer to record the time interval Δt between the direct sound and its echo.
3. The sound travels to the wall and back, a total distance of 2 d. Calculate the speed:
   v = 2d / Δt
4. Repeat the measurement for several distances and average the results to reduce random error.
5. Safety note: Keep the sound level moderate to protect hearing and avoid causing disturbance to neighbouring rooms; ensure the wall is solid and the area is clear of breakable objects.

Frequency, Pitch and Amplitude

• Frequency (f) – number of complete vibrations per second, measured in hertz (Hz).
   \(f = \dfrac{1}{T}\) where T is the period.
• Pitch – the perceived highness or lowness of a sound. Higher frequency → higher pitch (direct syllabus wording).
• Amplitude – maximum displacement of particles from equilibrium; it determines the pressure variation of the wave.
• Loudness – the perceived intensity of a sound. It increases with amplitude; **doubling the amplitude roughly raises the sound‑intensity level by 6 dB**.

Human Audible Frequency Range

The average healthy ear can detect frequencies from about ≈ 20 Hz to ≈ 20 kHz. Frequencies outside this range are classified as:

• Infrasound: < 20 Hz (e.g., earthquakes, volcanic eruptions).
• Ultrasound: > 20 kHz (e.g., bat echolocation, medical imaging, industrial cleaning).

Why the Audible Range Is Limited

1. The eardrum and cochlear hair cells are most responsive to vibrations between 20 Hz and 20 kHz.
2. At very low frequencies the particle displacement is too slow to stimulate the hair cells effectively.
3. At very high frequencies the wavelength becomes comparable to the dimensions of the inner‑ear structures, reducing detection efficiency.

Practical Activity – Determining Pitch

Activity: Use a set of tuning forks (e.g., 256 Hz, 440 Hz, 512 Hz). Strike each fork gently, hold it near a microphone, and record the sound with a simple spectrometer app on a tablet. Identify the dominant frequency displayed and match it to the known pitch of the fork. Discuss why the 440 Hz fork corresponds to the musical note A₄ and how changing the frequency changes the perceived pitch.

Summary

• Human audible range: ≈ 20 Hz – 20 kHz (≈ 20 Hz – 20 kHz for typical healthy ears).
• Sound is a longitudinal mechanical wave that requires a material medium.
• Speed of sound in air ≈ 330 – 350 m s⁻¹; it increases with temperature (~0.6 m s⁻¹ °C⁻¹) and is higher in liquids and solids.
• Frequency determines pitch (higher f → higher pitch); amplitude determines loudness (doubling amplitude ≈ +6 dB).
• Simple echo‑technique experiments can be used to measure the speed of sound safely in the classroom.
• Infrasound (< 20 Hz) and ultrasound (> 20 kHz) lie outside the audible range.