Calculating Displacement & Intensity of 1665 Hz Wave

[JasonV]

A sound wave has a frequency of 1665 Hz and a pressure amplitude of 1.13 x 10^-3 Pa. What were (a) the displacement amplitude and (b) the intensity of the wave emitted by the ear?

the equation i used for a is sm=delta(pm)/(vpw)

where p is the density, sm is the displacement amplitude, pm is the pressure amplitude, v is the velocity, and w is the angular frequency.

I could find all of the variables from the equation but the velocity (pm=1.13 x 10^-3, p=1.21, w=2pif=2pi x 1665)
Thanks in advance.

 

[Nate810]

a) The displacement amplitude is 5.25 x 10^-7 m.b) The intensity of the wave emitted by the ear is 1.34 x 10^-10 W/m2.

 

[ogb p]

I would first like to clarify that the equation provided is not a standard equation for calculating displacement amplitude. The correct equation for displacement amplitude (A) in a sound wave is A = pm/(p x v x w), where pm is the pressure amplitude, p is the density of the medium, v is the velocity of the wave, and w is the angular frequency.

Using this equation, we can calculate the displacement amplitude as follows:

A = (1.13 x 10^-3 Pa) / (1.21 kg/m^3 x v x 2π x 1665 Hz)

To solve for v, we can use the equation v = λ x f, where λ is the wavelength and f is the frequency. Since the frequency is given, we need to find the wavelength. The speed of sound in air is approximately 343 m/s, so we can use the equation λ = v/f to find the wavelength:

λ = (343 m/s) / (1665 Hz) = 0.206 m

Now, we can solve for v:

v = (0.206 m) x (1665 Hz) = 343 m/s

Plugging this value back into the original equation, we get:

A = (1.13 x 10^-3 Pa) / (1.21 kg/m^3 x 343 m/s x 2π x 1665 Hz) = 1.22 x 10^-10 m

Therefore, the displacement amplitude of the 1665 Hz sound wave is 1.22 x 10^-10 m.

To calculate the intensity of the wave, we can use the equation I = (pm)^2 / (2ρvw), where I is the intensity, pm is the pressure amplitude, ρ is the density of the medium, v is the velocity of the wave, and w is the angular frequency.

Plugging in the values, we get:

I = (1.13 x 10^-3 Pa)^2 / (2 x 1.21 kg/m^3 x 343 m/s x 2π x 1665 Hz) = 1.53 x 10^-9 W/m^2

Therefore, the intensity of the 1665 Hz sound wave is 1.53 x 10^-9 W/m^2. This is a relatively low intensity, as the threshold of human hearing is around 1 x