Calculating Nodal Lines for Water Tapping

[yinny]

Homework Statement

Two students are tapping their foot on the surface of the water in a pool

Distance between two point sources : 2m
length of the pool : 5m
freqency : 1Hz
v = 0.6m/s

How many nodal lines are created?

Homework Equations

lambda = v/f
d = (n-1/2)lambda

The Attempt at a Solution

First went for the wavelength:
lambda = v/f
lambda = 0.6/1
lambda = 0.6

Then went to find the "n"
d = (n-1/2) lambda
2 = (n-1/2) (0.6)
n-(1/2) = 2/0.6
n = (2/0.6) + (1/2)
n = 3.833

Then I don't know what to do next..D:

 

[anathema]

Thank you for your post. It seems like you are on the right track with your calculations so far. Let me help you continue with finding the number of nodal lines created by the two students tapping their foot on the water's surface.

First, let's review the concept of nodal lines. Nodal lines are the points on a wave where the amplitude is zero, resulting in no displacement. In this case, the two students tapping their feet act as point sources, creating circular waves that intersect and create nodal lines.

Based on your calculations, we know that the wavelength is 0.6m and the distance between the two point sources is 2m. This means that there are 3.833 wavelengths between the two point sources. Since each wavelength has two nodal lines (one at the beginning and one at the end), we can calculate the total number of nodal lines by multiplying the number of wavelengths by 2.

Therefore, the total number of nodal lines created by the two students tapping their foot on the water's surface is 3.833 x 2 = 7.666, or approximately 8 nodal lines.

I hope this helps you understand the concept of nodal lines and how to calculate their number in a given scenario. Keep up the good work in your scientific studies!

Scientist