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Ch 16: Sound & Hearing
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Capitolo 16, Problema 15a

A sound wave in air at 20°C has a frequency of 320 Hz and a displacement amplitude of 5.00 × 10-3 mm. For this sound wave calculate the pressure amplitude (in Pa)

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First, understand that the pressure amplitude of a sound wave is related to its displacement amplitude, frequency, and the properties of the medium (air in this case). The formula to calculate the pressure amplitude (ΔP) is: ΔP = ρ * v * ω * s₀, where ρ is the density of air, v is the speed of sound in air, ω is the angular frequency, and s₀ is the displacement amplitude.
Determine the density of air (ρ) at 20°C, which is approximately 1.204 kg/m³.
Calculate the speed of sound (v) in air at 20°C. The speed of sound in air can be approximated by the formula: v = 331.4 + 0.6 * T, where T is the temperature in Celsius. Substitute T = 20°C to find v.
Find the angular frequency (ω) using the formula: ω = 2 * π * f, where f is the frequency of the sound wave. Substitute f = 320 Hz to calculate ω.
Convert the displacement amplitude (s₀) from millimeters to meters by multiplying 5.00 * 10^-3 mm by 10^-3. Now, substitute all known values into the pressure amplitude formula: ΔP = ρ * v * ω * s₀, and solve for ΔP.

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Sound Wave Properties

Sound waves are longitudinal waves characterized by frequency, wavelength, amplitude, and speed. Frequency, measured in Hertz (Hz), indicates how many cycles occur per second. Amplitude refers to the maximum displacement of particles in the medium, affecting the wave's intensity and loudness.
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Standing Sound Waves

Pressure Amplitude

Pressure amplitude in a sound wave is the maximum change in pressure from the ambient atmospheric pressure caused by the wave. It is related to the displacement amplitude and frequency of the wave, and can be calculated using the formula involving the medium's density and speed of sound.
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Pressure and Atmospheric Pressure

Speed of Sound in Air

The speed of sound in air is influenced by temperature, with a typical value of approximately 343 meters per second at 20°C. This speed is crucial for calculating wave properties like wavelength and pressure amplitude, as it determines how quickly sound waves propagate through the medium.
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