16. Two point sources are generating periodic waves in phase. The wavelength of the waves is 3.0 cm. A point on a nodal line is 25 cm from one source and 20.5 cm from the other source. Construct a sketch of the physical situation and determine the nodal line number.

Here's how to solve this problem and determine the nodal line number:<br /><br />**1. Understanding Nodal Lines**<br /><br />Nodal lines are points where waves from two coherent sources interfere destructively. This destructive interference occurs when the path difference from the two sources to a point is an odd multiple of half the wavelength (λ/2).<br /><br />**2. Path Difference**<br /><br />The path difference in this case is 25 cm - 20.5 cm = 4.5 cm.<br /><br />**3. Calculating the Multiple of Half Wavelengths**<br /><br />To find which nodal line we're on, we divide the path difference by half the wavelength:<br /><br />4.5 cm / (3.0 cm / 2) = 4.5 cm / 1.5 cm = 3<br /><br />**4. Determining the Nodal Line Number**<br /><br />Since the result is 3 (an odd integer), this point lies on a nodal line. The number of the nodal line corresponds to the multiple of half wavelengths. Therefore, this point is on the **3rd nodal line**.<br /><br />**5. Sketch (Conceptual)**<br /><br />A precise sketch is difficult without specific angles, but a conceptual sketch would show:<br /><br />* Two point sources (labeled S1 and S2).<br />* A point P representing the point on the nodal line.<br />* Lines connecting S1 to P and S2 to P, representing the distances 25 cm and 20.5 cm, respectively.<br />* The nodal lines would be represented as curved lines emanating outwards from between the sources, with the 3rd nodal line passing through point P. The nodal lines alternate with antinodal lines (lines of constructive interference). The sketch should show the nodal lines getting further apart as they extend outward from the sources.<br /><br /><br />**Important Note:** The sketch is a visual aid. The calculation is the definitive way to determine the nodal line number.<br />