Frequency, Pitch and Ultrasonic Waves

Why this topic matters in CDS

Sound is one of the most dependable scoring areas in the CDS General Science paper. Almost every recent exam carries one or two questions on the properties of sound waves, and frequency-based questions are the most common of all. They are asked in both CDS (IMA, INA, AFA) and OTA papers, and the same ideas reappear in interviews and the SSB general-awareness chat.

The good news is that the concepts are short, formula-driven and rarely change from year to year. If you fix the definitions of frequency and pitch, memorise the audible range, learn the single wave equation, and remember a handful of ultrasonic applications, you can convert these into near-certain marks within seconds of reading the question.

This page builds the topic step by step, from what a sound wave actually is, through frequency, pitch and loudness, to the ultrasonic range and its uses. Two solved numericals and a previous-year-style question at the end show exactly how the examiner frames these ideas.

Sound as a longitudinal wave

When an object vibrates, it pushes the air particles next to it back and forth. These particles bump their neighbours, and a disturbance travels outward. The particles themselves do not move along with the sound; they only oscillate about their fixed positions.

Sound is a longitudinal wave: the particles vibrate parallel to the direction in which the wave moves. The wave travels as alternate regions of:

• Compression — particles crowded together, high pressure.
• Rarefaction — particles spread apart, low pressure.

One compression plus one adjacent rarefaction makes one complete wave (cycle). As the wave passes, the pressure at any point keeps rising and falling, so a sound wave can also be drawn as a pressure variation against distance. The crests of that curve are the compressions and the troughs are the rarefactions.

Because the particles only oscillate about fixed points and pass the energy along, sound transfers energy without transferring matter. The air in front of a loudspeaker does not stream towards you; only the disturbance does.

Frequency and time period

Frequency (f) is the number of complete vibrations (or waves) produced in one second. Its SI unit is the hertz (Hz), where 1 Hz = one vibration per second.

Time period (T) is the time taken to complete one vibration, measured in seconds.

Two more terms complete the picture:

• Amplitude — the maximum displacement of a particle from its rest position. It decides loudness.
• Wavelength (λ) — the distance between two consecutive compressions (or rarefactions). Its unit is the metre.

Larger multiples of the hertz are common in this topic: 1 kilohertz (kHz) = 1000 Hz, and 1 megahertz (MHz) = 10⁶ Hz.

The wave equation v = f × λ

The speed of a wave links the three quantities you have just met. In one time period the wave advances exactly one wavelength, so:

For a given medium at fixed temperature, the speed of sound is constant. So frequency and wavelength are inversely proportional: a higher frequency means a shorter wavelength.

Useful reference speeds of sound (at about 20°C to 25°C):

• In air: about 343 m/s (commonly rounded to 330–340 m/s).
• In water: about 1480 m/s.
• In steel/iron: about 5000–5960 m/s.

Pitch: how frequency reaches your ear

Pitch is the characteristic of sound that lets us tell a shrill note from a deep one. It is determined entirely by frequency.

• A high-frequency sound has high pitch — thin, shrill (a whistle, a child's voice, a flute).
• A low-frequency sound has low pitch — deep, heavy (a drum, a lion's roar, a man's voice).

This is why a woman's or child's voice usually sounds higher than a man's: the vocal cords vibrate at a greater frequency. The same logic explains a mosquito's thin buzz (high frequency, high pitch) against a bee's deeper hum (lower frequency, lower pitch). On a stringed instrument, a thinner, tighter or shorter string vibrates faster and so gives a higher pitch.

Do not confuse pitch with loudness. The three subjective qualities of a musical sound are:

• Pitch → depends on frequency.
• Loudness → depends on amplitude (and intensity).
• Timbre/quality → depends on the waveform, and lets us tell a violin from a flute playing the same note.

Loudness, intensity and the decibel

Loudness is how loud a sound seems to our ears. It grows with the amplitude of vibration — a string plucked harder vibrates with greater amplitude and sounds louder.

The physical measure behind loudness is intensity: the sound energy passing per second through unit area. Loudness is measured in decibels (dB).

• Normal conversation: about 60 dB.
• Busy traffic: about 70–80 dB.
• Sound above 80–85 dB for long periods can damage hearing; this is noise pollution.
• The threshold of hearing — the faintest sound a healthy ear can detect — is taken as 0 dB.

Loudness is partly subjective: the same sound seems louder in a quiet room than in a noisy market. Intensity, however, is a fixed physical quantity that falls as you move further from the source. This is why a distant train horn sounds faint even though it is physically very loud at the engine itself.

Infrasonic, audible and ultrasonic ranges

Human ears respond only to a limited band of frequencies. By this band, sound is divided into three ranges:

• Infrasonic (infrasound): below 20 Hz. Produced by earthquakes, volcanic activity, and large animals like whales, elephants and rhinos.
• Audible range: 20 Hz to 20,000 Hz (20 kHz) — the sound a healthy young human can hear.
• Ultrasonic (ultrasound): above 20,000 Hz (20 kHz). Inaudible to humans but produced and heard by bats, dolphins, dogs and porpoises.

Uses of ultrasonic waves

Ultrasonic waves travel in straight lines, carry high energy and can be focused into narrow beams. These properties give them many practical uses:

• SONAR (Sound Navigation And Ranging): ships send ultrasonic pulses into the sea and time the echo to find water depth, submarines, shoals of fish and sunken wrecks.
• Medical ultrasonography: scanning the foetus, heart (echocardiography), kidney stones and internal organs without surgery.
• Cleaning: removing dirt from delicate parts such as watches, jewellery and electronic components.
• Detecting flaws: finding cracks and air bubbles inside metal blocks and castings.
• Echolocation: bats and dolphins emit ultrasound and judge distance and direction from the returning echoes, letting bats fly and hunt in total darkness.

Notice that all of these rest on the same idea — the reflection of sound, or echo. An echo is heard distinctly only when the reflected sound returns after at least 0.1 second, which is why a clear echo needs the reflecting surface to be sufficiently far away. SONAR and medical scanning simply use ultrasonic echoes that are far too high in frequency for us to hear directly.

Worked example: SONAR depth

Worked example: frequency and wavelength

Previous-year style question

Other favourites from past papers include: the quality that decides pitch (frequency), the medium in which sound travels fastest (solids), and the principle behind SONAR (echo / reflection of ultrasonic waves).

Quick revision