SUMMARY
The displacement amplitude of a sound wave with a frequency of 160.0 Hz in air at 20 °C, given a pressure amplitude of 29.0 Pa, can be calculated using the formula s = ΔP/(β*k). The correct value for β is 1.4 x 10^5 Pa, and the wave speed Vs is 343 m/s. The wave number k is derived from the relationship k = f/Vs, but it should be noted that k is also defined as 2π/λ. The correct displacement amplitude is 4.44 x 10^-4 m, although the initial calculation was deemed incorrect due to misunderstanding the relationship between k and λ.
PREREQUISITES
- Understanding of sound wave properties, including frequency and pressure amplitude
- Familiarity with wave equations and relationships, specifically ΔP(x,t) = (ΔP)cos(kx - wt)
- Knowledge of the speed of sound in air at different temperatures
- Basic grasp of wave number and wavelength relationships, specifically k = 2π/λ
NEXT STEPS
- Study the derivation and application of the wave equation for sound waves
- Learn about the relationship between frequency, wavelength, and wave speed in different media
- Explore the concept of pressure amplitude in sound waves and its physical implications
- Investigate the effects of temperature on the speed of sound in air
USEFUL FOR
Students studying acoustics, physics educators, and anyone involved in sound wave analysis or related engineering fields.