Plane sound wave whose equation is in SI units

Let's consider the propagation of a plane sound wave in air with a density of 0.0012 g/cm^3. The equation of a sound wave in SI units is:

y(x,t) = 2,5*10^-6 * cos(10^3*П*(t-(x/330)))

where x is the coordinate of a point on the wave propagation axis in meters, t is time in seconds.

The average value of the squared sine for the period is 0.5. Let's find the energy carried by a sound wave in one minute through an area of ​​12 cm^2, perpendicular to the propagation of the wave.

To solve the problem, we use the formula for the energy of a sound wave:

W = (p*y^2*v*S*T)/2

where p is the density of the medium, y is the amplitude of vibrations, v is the speed of sound propagation in the medium, S is the area perpendicular to the direction of sound propagation, T is the period of vibration.

The amplitude y value is found from the sound wave equation:

y = 2,5*10^-6

The speed of sound propagation in air at room temperature and atmospheric pressure is approximately 330 m/s.

We find the oscillation period T, knowing the frequency f:

T = 1/f

Frequency f is:

f = 10^3*П

The area S is 12 cm^2, i.e. 0.0012 m^2.

Now we can find the energy of the sound wave:

W = (0.0012* (2.5*10^-6)^2 * 330 * 0.0012 * (1/(10^3*P))) / 2 = 4.47*10^-11 J

Thus, the energy carried by a sound wave in one minute through an area of ​​12 cm^2, perpendicular to the propagation of the wave, is equal to 2.68 * 10^-9 J.

Task 40588

The equation of the sound wave and the density of the medium are given. The energy carried by a wave in one minute through an area of ​​12 cm^2, perpendicular to the propagation of the wave, was found, taking into account the average value of the square of the sine for the period.

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Our product is a plane sound wave, the equation of which in SI units is y(x,t)= 2.510^-6 * cos(10^3P*(t-(x/330))). This wave propagates in air with a density of 0.0012 g/cm^3 and is capable of transferring energy through an area of ​​12 cm^2, perpendicular to the propagation of the wave, in one minute.

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This digital product is a plane sound wave that propagates in air with a density of 0.0012 g/cm^3. The equation for a sound wave in SI units is y(x,t)= 2.5*10^-6 * cos10^3 Pi(t-(x/330)). This wave is capable of transferring energy through an area of ​​12 cm^2, perpendicular to the propagation of the wave, in one minute.

To determine the energy carried by a wave in one minute through an area of ​​12 cm^2, perpendicular to the propagation of the wave, we can use the formula for the energy of a sound wave: W = (py^2vST)/2, where p is the density of the medium, y is the amplitude of vibrations, v is the speed of sound propagation in the medium, S is the area perpendicular to the direction of sound propagation, T is the period of vibration.

The amplitude value y is found from the sound wave equation: y = 2.510^-6. The speed of sound propagation in air at room temperature and atmospheric pressure is approximately 330 m/s. We find the oscillation period T, knowing the frequency f: T = 1/f. Frequency f is 10^3P. The area S is 12 cm^2, i.e. 0.0012 m^2.

Now we can find the energy of the sound wave: W = (0.0012 * (2.510^-6)^2 * 330 * 0,0012 * (1/(10^3P))) / 2 = 4.47*10^-11 J.

Thus, the energy carried by a sound wave in one minute through an area of ​​12 cm^2, perpendicular to the propagation of the wave, is equal to 2.68 * 10^-9 J.

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It is a flat sound wave that propagates in air with a density of 0.0012 g/cm³. The equation for this sound wave in SI units is y(x,t) = 2.510^-6cos(10^3π(t-(x/330))), where x is the coordinate of a point on the wave, t is time, π is a mathematical constant, cos is cosine, and 10^3 is the number 1000.

To calculate the energy carried by a wave in one minute through an area of ​​12 cm², perpendicular to the propagation of the wave, the following formula must be used:

E = (1/2)rvAΔt*,

where E is the energy carried by the wave, ρ is the density of the medium, v is the speed of sound, A is the area, Δt is time, ω is the angular frequency, is the average value of the square of the sine over the period.

To solve this problem, it is necessary to substitute the known values: ρ = 0.0012 g/cm³, A = 12 cm² = 1.2*10^-3 m², v = 330 m/s (speed of sound in air at room temperature), Δt = 60 s (one minute), as well as angular frequency ω = 10^3π rad/s.

To calculate the value of , you can use the problem condition, which states that the average value of the squared sine over the period is 0.5.

Thus, by calculating all the known values ​​and substituting them into the formula, we obtain the value of the energy carried by the wave in one minute through an area of ​​12 cm², perpendicular to the propagation of the wave.

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