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 node of the resultant standing wave, we need to find the points where the two waves interfere destructively, i.e., the amplitudes subtract from each other. This occurs at half-wavelength intervals of the standing wave.

Let's first find the wavelength of each wave:
Wave 1: wavelength = 22/5 cm = 4.4 cm
Wave 2: wavelength = 22/4 cm = 5.5 cm

The wavelengths are not the same, so we need to find the least common multiple (LCM) to determine the distance between consecutive nodes. 
The LCM of 4.4 and 5.5 is 22 cm.

So, the distance between consecutive nodes is 22 cm / 2 = 11 cm.

Therefore, the smallest positive value of x corresponding to a node of the resultant standing wave is 0 cm (at x = 11 cm), which is the midpoint between two nodes. Thus, the answer is choice C.

Two Harmonic Waves Are Described By: from the Choices