Sound waves are vibrations that travel through air, water, and solids. They're characterized by amplitude, frequency, wavelength, and speed. These properties determine how loud or high-pitched a sound is and how fast it moves.

The speed of sound depends on what it's traveling through. It moves faster in denser, more elastic materials. Temperature also affects sound speed in gases. Understanding these factors helps us grasp how sound behaves in different environments.

Sound Wave Characteristics and Behavior

Characteristics of sound waves

• Sound waves propagate as longitudinal waves
  • Particles in the medium vibrate parallel to the direction of wave propagation causing compressions (high pressure regions) and rarefactions (low pressure regions) to alternate
• Sound waves require a medium to propagate and cannot travel through a vacuum
• Sound waves transfer energy through the medium without transferring matter
• Sound wave characteristics include:
  • Amplitude determines the loudness of the sound and represents the maximum displacement of particles from their equilibrium position
  • Frequency ($f$) measured in Hertz (Hz) determines the pitch of the sound and represents the number of wave cycles passing a fixed point per unit time
  • Wavelength ($\lambda$) measured in meters (m) represents the distance between two consecutive compressions or rarefactions
  • Speed ($v$) measured in meters per second (m/s) represents the rate at which the sound wave propagates through the medium

Factors affecting sound speed

• The speed of sound depends on the properties of the medium it travels through
  • Density ($\rho$) represents the mass per unit volume of the medium and denser materials generally have slower sound speeds
  • Elasticity (bulk modulus, $B$) measures a material's resistance to compression and more elastic materials have faster sound speeds
• Speed of sound in a medium is given by: $v = \sqrt{\frac{B}{\rho}}$
• Speed of sound in gases:
  • Depends on temperature with higher temperatures resulting in faster sound speeds (at 20°C or 68°F, the speed of sound in air is approximately 343 m/s or 1,125 ft/s)
• Speed of sound in liquids and solids:
  • Generally faster than in gases due to higher density and elasticity (in water at 20°C, the speed of sound is about 1,482 m/s or 4,862 ft/s and in steel, the speed of sound is around 5,960 m/s or 19,550 ft/s)

Speed, frequency and wavelength relationships

• The speed ($v$), frequency ($f$), and wavelength ($\lambda$) of a sound wave are related by the equation: $v = f\lambda$ (also known as the wave equation)
  • Speed is measured in meters per second (m/s), frequency is measured in Hertz (Hz), and wavelength is measured in meters (m)
• To find the wavelength, use: $\lambda = \frac{v}{f}$
  • If a sound wave has a frequency of 440 Hz and travels at 343 m/s, its wavelength is $\lambda = \frac{343 \text{ m/s}}{440 \text{ Hz}} \approx 0.78 \text{ m}$
• To find the frequency, use: $f = \frac{v}{\lambda}$
  • If a sound wave has a wavelength of 1.5 m and travels at 1,482 m/s in water, its frequency is $f = \frac{1,482 \text{ m/s}}{1.5 \text{ m}} \approx 988 \text{ Hz}$

Wave propagation and interaction

• Sound waves propagate through a medium by creating alternating regions of high and low pressure
• The vibration of particles in the medium transfers energy from one point to another
• Resonance occurs when an object or system is forced to vibrate at its natural frequency, leading to increased amplitude
• Different media (e.g., air, water, steel) affect how sound waves propagate due to variations in their physical properties