Create a mathematical model for the pressure variation as a function of position and time for a sound wave, given that the wavelength of the wave is λ = 0.190 m and the maximum pressure variation is ΔPmax = 0.270 N/m2. Assume the sound wave is sinusoidal. (Assume the speed of sound is 343 m/s. Use the following as necessary: x and t. Assume ΔP is in Pa and x and t are in m and s, respectively. Do not include units in your answer.)

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CarliReifsteck CarliReifsteck · Answer 1 · 2019-09-16T11:16:40+02:00

Answer:

The equation of position and time for a sound wave is [tex]\Delta p=0.270(33.06 x-11342.40 t)[/tex].

Explanation:

Given that,

Wavelength = 0.190 m

Maximum pressure [tex]\Delta P_{max}= 0.270 N/m^2[/tex]

We know that,

The function of position and time for a sound wave,

[tex]\Delta p=\Delta p_{max}(kx-\omega t)[/tex]....(I)

We need to calculate the frequency

Using formula of frequency

[tex]f=\dfrac{v}{\lambda}[/tex]

Put the value into the formula

[tex]f=\dfrac{343}{0.190}[/tex]

[tex]f=1805.2\ Hz[/tex]

We need to calculate the angular frequency

Using formula of angular frequency

[tex]\omega =2\pi f[/tex]

Put the value into the formula

[tex]\omega=2\pi\times1805.2[/tex]

[tex]\omega=11342.40\ rad/s[/tex]

We need to calculate the wave number

Using formula of wave number

[tex]k = \dfrac{2\pi}{\lambda}[/tex]

Put the value into the formula

[tex]k=\dfrac{2\pi}{0.190}[/tex]

[tex]k=33.06[/tex]

Now, put the value of k and ω in the equation (I)

[tex]\Delta p=0.270(33.06 x-11342.40 t)[/tex]

Hence, The equation of position and time for a sound wave is [tex]\Delta p=0.270(33.06 x-11342.40 t)[/tex].