Question

Smax (13%) Problem 6: A periodic vibration at x = 0,t=0 displaces air molecules along the x direction by Smax = 5.5E-05 m. The motion produces a sound wave that travels at a velocity of v= 350 m's with a frequency of 7-145 Hz. Take the density of air as Pa = 1.20 kg/m?. x=0 Otheexpertta.com 14% Part (a) Calculate the wavelength of the sound wave, in meters. 2-2.413 Correct! 14% Part (b) Calculate the wavenumber k of the sound, in radians per meter. k= 2.603 ✓ Correct! 14% Part (c) Calculate the angular frequency of the sound o, in radians per second. 0-911.062 w = 911.1 ✓ Correct! > *14% Part (d) Calculate the displacement of the air molecules using an function for the traveling sound wave in terms of time and position at time t = 0.001 s and displacement x = 1.0 m. s(1,0.001)= 5.45 + 10-5| Potential 90% Grade Summary Deductions 10% sin cos tan ( 7 8 9 HOME EA4 6 1 2 3 cotan asino acoso atan acotan sinh cosho tanho cotanh Degrees Radians Submissions Attempts remaining: 2 (2% per attempt) detailed view 1 2% 2% 2% + 0 END 2 VO BACKSPACE DEL CLEAR درا

Feedback:

-Check the units carefully, particularly inside the trig function.

Hints:

-What function describes a wave traveling in the positive x-direction that starts with a positive displacement of s_max?
-Be very careful how you calculate this - if you approximate π as 3.14 you may not be accurate enough, since you are evaluating a trig function of a very small value.
-Watch the units - your calculate must be set in radians!

Answer 1

Answer:

(d) The required function is s(x,t) = s_max cos(kx-$\omega$t)

Given that s_max = 5.5E^-05 m = 5.5 x 10^-5 m

Using the answers of part (b) and (c)

wavenumber k = 2.603 rad/m and angular frequency $\omega$ = 911.1 rad/s

Thus, s(x,t) = (5.5 x 10^-5 m) cos[(2.603 rad/m) x - (911.1 rad/s) t]

At x = 1.0 m and t = 0.001 s, the displacment will be

Therefore,

s(1,0.001) = (5.5 x 10^-5 m) cos[(2.603 rad/m) (1.0 m) - (911.1 rad/s) (0.001 s)]

                = (5.5 x 10^-5 m) (-0.1208)

               = -6.64 x 10^-6 m