Sound — SOF NSO Study Notes

Overview

Sound is a mechanical wave that travels through a medium by creating vibrations. This topic consistently appears in NSO with 3–5 questions testing conceptual understanding, numerical calculations and real-world applications. Students must understand how sound is produced, how it travels, what makes sounds different from each other (pitch, loudness, quality), and phenomena like reflection and echo.

The NSO specifically tests production mechanisms (vibrating objects), propagation requirements (need for a medium, speed variations), wave characteristics (frequency, amplitude, wavelength), and practical applications like echo ranging and sound reflection in halls. Questions often involve calculating distances using echo time, comparing speeds in different media, or identifying which properties change when sound characteristics change. Mastery requires both conceptual clarity and comfort with the relationship: speed = distance/time and speed = frequency × wavelength.

Key Concepts

• **Sound is a mechanical wave** — It requires a material medium (solid, liquid or gas) to travel. Sound cannot propagate through vacuum because there are no particles to vibrate.

• **Production by vibration** — All sound originates from vibrating objects. When an object vibrates, it creates compressions (high pressure regions) and rarefactions (low pressure regions) in the surrounding medium, forming a longitudinal wave.

• **Speed varies with medium** — Sound travels fastest in solids (particles are closely packed), slower in liquids, and slowest in gases. In air at 20°C, speed ≈ 344 m/s; in water ≈ 1500 m/s; in steel ≈ 5000 m/s. Speed increases with temperature in gases.

• **Pitch depends on frequency** — High frequency sounds have high pitch (like a whistle), low frequency sounds have low pitch (like a drum). Human hearing range: 20 Hz to 20,000 Hz. Sounds below 20 Hz are infrasonic; above 20,000 Hz are ultrasonic.

• **Loudness depends on amplitude** — Greater amplitude means more energy and louder sound. Loudness is measured in decibels (dB). Normal conversation ≈ 60 dB; threshold of pain ≈ 120 dB.

• **Quality (timbre) distinguishes sources** — Even at the same pitch and loudness, a flute and violin sound different due to quality, which depends on the waveform and presence of overtones (harmonics).

• **Echo is reflected sound** — When sound reflects off a hard surface and returns to the listener with a time gap, it's heard as an echo. Minimum distance needed: 17 m (for 0.1 s distinction time in air).

• **Reverberation vs echo** — Reverberation is prolonged reflection causing persistence of sound in enclosed spaces. Unlike distinct echoes, reverberations blend together creating a continuous effect.

Formulas / Key Facts

**Speed of sound:** Speed = Distance / Time Context: Used in echo calculations and distance measurements.

**Wave equation:** Speed = Frequency × Wavelength (v = f × λ) Context: Relates wave properties; if frequency increases, wavelength decreases (for constant speed).

**Echo distance formula:** Distance to reflecting surface = (Speed × Time) / 2 Context: Factor of 2 because sound travels to the surface and back.

**Minimum distance for echo:** 17.2 m in air at normal conditions Context: Based on 0.1 s persistence of sound in human ear and speed ≈ 344 m/s.

**Audible frequency range:** 20 Hz to 20,000 Hz for humans Context: Below 20 Hz = infrasonic (elephants, earthquakes); above 20,000 Hz = ultrasonic (bats, dolphins, medical imaging).

**Speed in different media:** Solid > Liquid > Gas Context: Steel (~5960 m/s) > Water (~1500 m/s) > Air (~344 m/s at 20°C).

**Decibel scale:** Logarithmic scale for sound intensity Context: 0 dB = threshold of hearing; 120 dB = threshold of pain; 10 dB increase ≈ sound appears twice as loud.

Worked Examples

**Example 1: Echo Calculation** A person shouts near a cliff and hears an echo after 3 seconds. If speed of sound is 340 m/s, how far is the cliff?

*Solution:*

• Total distance traveled by sound = Speed × Time = 340 × 3 = 1020 m
• This is the distance to the cliff and back (two-way journey)
• Distance to cliff = 1020 / 2 = **510 m**

**Example 2: Frequency-Wavelength Relationship** A sound wave travels in air at 340 m/s with wavelength 0.68 m. Calculate its frequency and identify if humans can hear it.

*Solution:*

• Using v = f × λ
• 340 = f × 0.68
• f = 340 / 0.68 = 500 Hz
• Since 500 Hz is between 20 Hz and 20,000 Hz, **yes, humans can hear it**

**Example 3: Medium Comparison** A sound pulse travels 1500 m in water in 1 second. If the same sound travels in air at 340 m/s, how much time would it take to cover the same distance?

*Solution:*

• Speed in water = 1500 / 1 = 1500 m/s (verification)
• Time in air = Distance / Speed = 1500 / 340 = 4.41 seconds
• Sound takes **about 4.4 times longer in air** than in water

Common Mistakes

**Mistake:** Thinking sound can travel through vacuum → **Fix:** Sound is a mechanical wave requiring particles to vibrate. Space is silent; astronauts use radio waves (electromagnetic) to communicate.

**Mistake:** Confusing pitch with loudness → **Fix:** Pitch relates to frequency (how high or low), loudness relates to amplitude (how strong). A whisper can be high-pitched but soft.

**Mistake:** Forgetting the factor of 2 in echo distance problems → **Fix:** Sound travels to the obstacle AND back. Always divide the total distance by 2 to find distance to the reflecting surface.

**Mistake:** Assuming speed of sound is constant everywhere → **Fix:** Speed depends on medium and temperature. Speed increases in denser solids, and in air, speed increases by about 0.6 m/s per °C rise in temperature.

**Mistake:** Thinking higher frequency means louder sound → **Fix:** Frequency and amplitude are independent. A low-frequency drum beat can be louder than a high-frequency whistle.

Quick Reference

• Sound = longitudinal mechanical wave; needs medium; travels as compressions and rarefactions
• Speed: Solid > Liquid > Gas; in air ≈ 340 m/s
• Pitch ∝ frequency; Loudness ∝ amplitude; Quality = waveform/harmonics
• Audible range: 20–20,000 Hz; infrasonic < 20 Hz; ultrasonic > 20,000 Hz
• Echo: Distance to surface = (Speed × Time) / 2; minimum 17 m for distinct echo
• v = f × λ — if frequency increases, wavelength decreases (for constant speed)