Two harmonic waves are described by

From the choices given,determine the smallest positive value of x (in cm)corresponding to a node of the resultant standing wave.
A)3
B)0.25
C)0
D)6
E)1.5

Question

Two harmonic waves are described by

From the choices given,determine the smallest positive value of x (in cm)corresponding to a node of the resultant standing wave.
A)3 
B)0.25 
C)0 
D)6 
E)1.5

Quizplus · Accepted Answer

To find the nodes of the standing wave, we need to add the two waves and set it equal to zero.

11ea7ff9_2b8e_e2e9_a768_5f9729e490d9_TB2295_00 + 11ea7ff9_2b8f_09fa_a768_4554222ce64b_TB2295_00 = 2Acos(kx)sin(wt) = 0

Since we're looking for the smallest positive value of x, we want to find the first node of the standing wave, which occurs when the sine function is equal to zero. This happens when kx = n*pi, where n is an integer.

So, kx = n*pi

Solving for x:

x = n*pi/k

The smallest value of x will occur when n = 0, which gives:

x = 0

Therefore, the answer is C (0).

Two Harmonic Waves Are Described by