The displacement of the air molecules in a sound wave is modeled with the wave function s(x, t) = 3.00 nm cos(50.00 m−1x − 1.71 ✕ 104 s−1t). (a) What is the wave speed (in m/s) of the sound wave? 342 Correct: Your answer is correct. m/s (b) What is the maximum speed (in m/s) of the air molecules as they oscillate in simple harmonic motion? m/s (c) What is the magnitude of the maximum acceleration (in m/s2) of the air molecules as they oscillate in simple harmonic motion?

a) 342 m/s

b) 51*10^-6 m/s

c) 0.87m/s^2

Explanation:

The following function describes the displacement of the molecules in a sound wave:

 (1)

The general form of a function that describes the same situation is:

  (2)

By comparing equations (1) and (2) you have:

k: wave number = 50.00 m^-1

w: angular frequency = 1.71*10^4 s^-1

A: amplitude of the oscillation = 3.00nm

a) The speed of the sound is obtained by using the formula:

b) The maximum speed of the molecules is the maximum value of the derivative of s(x,t), in time. Then, you first obtain the derivative:

The max value is:

= 51*10^-6 m/s

c) The acceleration is the max value of the derivative of the speed, that is, the second derivative of the displacement s(x,t):

Then, the maximum acceleration is:

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.