sound - Important Formulas, Definitions, and Examples | 11th Physics

Chapter 8: Sound

Formulas: Speed of Sound, Wavelength, Frequency, Amplitude, Wave Equation

Introduction

Sound is a form of energy that travels as waves through different media, such as air, water, or solids. This chapter covers the properties of sound, its transmission, and various characteristics including frequency, wavelength, and amplitude.

1. Nature of Sound Waves

Definition:

Sound is a mechanical wave that requires a medium for propagation. It is produced by vibrating objects, and the vibration of particles within a medium enables sound to travel.

• Sound waves are longitudinal waves in which particle displacement is parallel to wave propagation.
• Sound cannot travel through a vacuum, as it requires a medium with particles.

2. Speed of Sound

Definition:

The speed of sound depends on the medium through which it travels and is faster in solids than in liquids or gases. In air, sound travels at approximately 343 m/s at room temperature.

• Formula: v = f × λ, where v is the speed of sound, f is the frequency, and λ is the wavelength.

3. Frequency, Wavelength, and Amplitude

Definitions:

• Frequency (f): The number of oscillations or cycles per unit time, measured in Hertz (Hz).
• Wavelength (λ): The distance between two consecutive points in phase on a wave, such as crest to crest or trough to trough.
• Amplitude: The maximum displacement from the equilibrium position, indicating the loudness of sound.

The relationship between frequency and wavelength is given by the formula: v = f × λ.

4. Wave Equation for Sound

Definition:

The wave equation is a mathematical representation of wave properties, and it can be used to describe sound waves.

• Formula: y(x, t) = A sin(kx - ωt + φ)
• Where y(x, t) is the displacement, A is the amplitude, k is the wave number, ω is the angular frequency, t is time, and φ is the phase constant.

5. Intensity of Sound

Definition:

The intensity of sound is the power per unit area carried by a sound wave, often measured in watts per square meter (W/m²).

• It is proportional to the square of the amplitude and inversely proportional to the square of the distance from the source.

6. Reflection, Refraction, and Diffraction of Sound

Definitions:

Sound waves can undergo reflection, refraction, and diffraction when they encounter obstacles or changes in medium:

• Reflection: Sound waves bounce back when they hit a solid surface, creating echoes.
• Refraction: The bending of sound waves as they pass through mediums of different densities.
• Diffraction: The bending of sound waves around obstacles or through openings.

7. Doppler Effect

Definition:

The Doppler Effect refers to the change in frequency or wavelength of a wave as observed by someone moving relative to the source of the sound. This effect is commonly heard in the change of pitch of a moving siren or vehicle.

• Formula: f' = f × (v + vo) / (v - vs), where f' is the observed frequency, f is the source frequency, v is the speed of sound, vo is the observer's speed, and vs is the source's speed.