Study Notes: Sound and Waves

Overview

Sound and Waves is a core Physics topic in Railway Group D that combines fundamental wave concepts with everyday phenomena like echo, loudness, and ultrasound applications. This chapter typically yields 2–3 direct questions in the General Science section, testing both theoretical understanding and practical applications.

Students must understand that sound is a mechanical wave requiring a medium (solid, liquid, or gas) to travel. Unlike light, sound cannot propagate through vacuum. The topic covers wave characteristics (frequency, wavelength, amplitude), reflection producing echoes, refraction causing direction changes, and real-world applications in SONAR, medical ultrasonography, and architectural acoustics.

Mastery requires knowing numerical relationships (speed = frequency × wavelength), recognizing which factors affect sound speed in different media, and applying reflection principles to calculate distances using echo time. Questions often test the distinction between longitudinal (sound) and transverse (light) waves, audible frequency ranges, and practical uses of ultrasound beyond human hearing range.

Key Concepts

• **Sound is a longitudinal mechanical wave** where particles vibrate parallel to wave direction, creating compressions (high pressure) and rarefactions (low pressure). Unlike transverse waves (light, water surface waves), sound particles oscillate back-and-forth along propagation path.

• **Medium requirement**: Sound needs material particles to transfer energy. Speed varies by medium density and elasticity: fastest in solids (~5000 m/s in steel), slower in liquids (~1500 m/s in water), slowest in gases (~343 m/s in air at 20°C). Sound cannot travel through vacuum.

• **Wave properties**: Frequency (Hz) = vibrations per second; wavelength (λ) = distance between consecutive compressions; amplitude = maximum particle displacement determining loudness. These relate as: Speed (v) = Frequency (f) × Wavelength (λ).

• **Audible range**: Human ear detects 20 Hz to 20,000 Hz. Infrasound (<20 Hz) produced by earthquakes, whales; ultrasound (>20,000 Hz) used in SONAR, medical imaging. Dogs hear up to 50,000 Hz, bats up to 100,000 Hz.

• **Reflection of sound** follows laws identical to light: angle of incidence equals angle of reflection. Produces echoes when reflected sound reaches listener distinctly after direct sound (minimum 0.1 second gap needed, requiring 17 m minimum distance).

• **Refraction of sound** occurs when passing between media of different densities, bending toward the normal when entering denser medium. Explains why sound travels farther at night (air layers of different temperatures refract sound downward).

• **Intensity and loudness**: Intensity (energy per unit area) measured in W/m²; loudness (subjective perception) measured in decibels (dB). Normal conversation = 60 dB, threshold of pain = 120 dB. Doubling distance quarters intensity (inverse square law).

Formulas / Key Facts

• **Speed of sound in air**: v = 331 + 0.6T m/s, where T = temperature in °C. At 20°C: v ≈ 343 m/s.

• **Fundamental wave equation**: v = f × λ (Speed = Frequency × Wavelength). All three quantities inversely/directly related.

• **Echo distance formula**: Distance = (Speed × Time) / 2. Divide by 2 because sound travels to obstacle and back.

• **Speed hierarchy**: v(solid) > v(liquid) > v(gas). Example: Steel (5960 m/s) > Water (1480 m/s) > Air (343 m/s).

• **Audible range**: 20 Hz – 20,000 Hz (humans). Infrasound <20 Hz; Ultrasound >20,000 Hz.

• **Persistence of hearing**: Human ear retains sound sensation for 0.1 second. Echo heard distinctly only if reflected sound arrives after this gap (minimum 17 m distance at 343 m/s).

• **Doppler Effect**: Apparent frequency increases when source approaches observer, decreases when receding. Used in speed guns, astronomy.

• **SONAR formula**: Depth = (Speed × Time) / 2. Time measured from emission to echo reception.

Worked Examples

**Example 1**: A person standing between two cliffs claps hands and hears two echoes after 2 seconds and 3 seconds. Speed of sound = 340 m/s. Find distance to each cliff.

*Solution*: For first cliff: Distance = (Speed × Time) / 2 = (340 × 2) / 2 = 340 m For second cliff: Distance = (340 × 3) / 2 = 510 m **Answer**: Cliffs are 340 m and 510 m away.

**Example 2**: A sound wave has frequency 500 Hz and wavelength 0.68 m. Calculate its speed and identify the medium.

*Solution*: Using v = f × λ v = 500 × 0.68 = 340 m/s This speed corresponds to sound in air at approximately 15°C. **Answer**: 340 m/s; medium is air.

**Example 3**: Why can we hear sound around corners but cannot see around them?

*Solution*: Sound wavelengths (1 cm to 10 m) are comparable to everyday obstacles like doors, walls. This causes significant diffraction (bending around edges). Light wavelengths (~500 nanometers) are extremely small compared to obstacles, producing negligible diffraction. Sound diffracts easily; light travels in straight lines. **Answer**: Sound's longer wavelength causes greater diffraction than light.

Common Mistakes

• **Confusing speed with loudness**: Students think louder sounds travel faster. *Correction*: Speed depends only on medium properties (temperature, density, elasticity). Loudness relates to amplitude, not speed. A whisper and shout travel at same 343 m/s in air.

• **Forgetting the "divide by 2" in echo problems**: Calculating distance using total time without accounting for round trip. *Correction*: Sound travels to obstacle AND back. Always use Distance = (v × t) / 2, not v × t.

• **Mixing up longitudinal and transverse**: Stating sound is a transverse wave like light. *Correction*: Sound particles vibrate parallel to direction (longitudinal). Only transverse waves have perpendicular particle motion. This is why sound cannot be polarized.

• **Assuming sound travels in vacuum**: Believing sound propagates through space like electromagnetic waves. *Correction*: Sound requires material medium. Space is silent—astronauts use radio waves (electromagnetic) for communication.

• **Misapplying ultrasound range**: Claiming frequencies like 15,000 Hz or 25,000 Hz are ultrasound. *Correction*: Ultrasound strictly means >20,000 Hz. 15,000 Hz is audible (high-pitched). Medical ultrasound uses 1–15 MHz, far beyond audibility.

Quick Reference

• Sound = longitudinal mechanical wave; needs medium; cannot travel through vacuum.
• Speed in air at 20°C = 343 m/s; increases 0.6 m/s per °C rise; fastest in solids.
• Audible range: 20–20,000 Hz; infrasound <20 Hz; ultrasound >20,000 Hz.
• Echo formula: Distance = (Speed × Time) / 2 (divide by 2 for round trip).
• v = f × λ connects speed, frequency, wavelength.
• Reflection: angle in = angle out; Refraction: sound bends entering different medium.
• Applications: SONAR (sea depth), ultrasound (medical imaging, cleaning), echo-ranging.