Question

A traveling sound wave through the air is given by s(x,t) = (9.0nm)cos(kx+(1500 r ad s )t +φ). How long would it take for the air molecule to move between +5.0nm and −5.0nm?

Hints:

• Note that you are dealing with a function of two variables, x and t. Choose convenient values for s,x, and t to first determine φ.

• Assign one of the value for s(t) that is given in the problem, and solve for t. (Keep the calculator in radian mode.)

• Now that you know how long it takes to go to the assigned value from your initial value, find the total time needed to go from one given value to another.

Answer 1

The equation is given by

Suppose that s = 9.0 nm (maximum value) at x = 0 ant t = 0.

Then,

substituting the value of x and t in the equation,

Using s = 9.0 nm,

We will consider the value at x = 0 only.

At a time t,

s(x = 0, t) is given by

Let s = +5 nm at t = t1.

Then,

Then,

Let s = -5 nm at t = t2.

Then,

Similarly,

The time taken is