Consider a scenario where a sound wave of frequency 100 Hz is produced by a tuning fork. The wave propagates through a medium with a speed of 340 m/s. The pressure amplitude of the wave is measured to be 0.2 Pa.
(a) Calculate the wavelength of the sound wave.
(b) Determine the energy density of the sound wave.
(c) If the intensity of the sound wave at a certain distance is measured to be 2.5 W/m^2, what is the sound level in dB at this distance?
(a) To find the wavelength of the sound wave, we can use the equation:
wavelength = speed / frequency
Plugging in the values:
wavelength = 340 m/s / 100 Hz
Therefore, the wavelength of the sound wave is 3.4 meters.
(b) The energy density of a sound wave can be calculated using the equation:
energy density = (pressure amplitude)^2 / (2 * density * wave speed^2)
The density of air is approximately 1.2 kg/m^3.
Plugging in the values:
energy density = (0.2 Pa)^2 / (2 * 1.2 kg/m^3 * (340 m/s)^2)
Simplifying the expression:
energy density = 0.044 Pa^2 / (2 * 1.2 kg/m^3 * (340 m/s)^2)
Therefore, the energy density of the sound wave is approximately 2.254 × 10^-6 J/m^3.
(c) The sound level in decibels (dB) can be calculated using the equation:
sound level = 10 * log10(intensity / reference intensity)
The reference intensity is 1 × 10^-12 W/m^2.
Plugging in the values:
sound level = 10 * log10(2.5 W/m^2 / (1 × 10^-12 W/m^2))
Simplifying the expression:
sound level = 10 * log10(2.5 × 10^12)
sound level = 10 * 12.398 Therefore, the sound level at this distance is approximately 123.98 dB.