Wave Interference Pattern Question

[wilson_chem90]

A two-point source operates at a frequency of 1.0 Hz to produce an interference pattern in a ripple tank. The sources are 2.5 cm apart and the wavelength of the waves is 1.2 cm.

Calculate the angles at which the nodal lines in the pattern are far from the sources. (Assume the angles are measured from the central line of the pattern).



Relevant equations:
dsinO = (n-1/2)(wavelength)

O = angle theta


my problem is, is that i can't figure out how many nodal lines there are in order to do the question. I know once i rearrange the equation i can find the angle, by the way i rearranged it to be O = sin inverse [(n-1/2)(wavelength)/d}.

 

[Nate810]

Is there a formula to find out the number of nodal lines? Yes, there is a formula to find the number of nodal lines. The formula is given by: n = (2d/wavelength) + 1, where d is the distance between the two sources and wavelength is the wavelength of the waves. Using this formula, we can calculate the number of nodal lines for the given data as: n = (2*2.5 cm / 1.2 cm) + 1 = 3 nodal lines. Once you have calculated the number of nodal lines, you can use the equation: O = sin inverse [(n-1/2)(wavelength)/d] to calculate the angles at which the nodal lines in the pattern are located from the sources. For the given data, the angles will be: O1 = sin inverse [(3-1/2)(1.2 cm)/2.5 cm] = 45 degreesO2 = sin inverse [(2-1/2)(1.2 cm)/2.5 cm] = 63.43 degreesO3 = sin inverse [(1-1/2)(1.2 cm)/2.5 cm] = 90 degrees

 

[tomcue]

Dear student,

Thank you for your question. The number of nodal lines in an interference pattern is dependent on the number of sources and the distance between them. In this case, there are two sources and the distance between them is 2.5 cm. Using the equation you provided, we can calculate the angle at which the nodal lines are located.

First, we need to determine the number of nodal lines present in the pattern. This can be done by rearranging the equation to solve for n:

n = (2dsinO/wavelength) + 1

Plugging in the values given in the problem, we get:

n = (2*2.5 cm*sinO)/(1.2 cm) + 1

n = 4.17 + 1

n = 5.17

Since we cannot have a fraction of a nodal line, we can round down to get a total of 5 nodal lines in the pattern.

Now, we can use this value of n in the equation you rearranged to find the angle at which the nodal lines are located:

O = sin^-1 [(n-1/2)(wavelength)/d]

O = sin^-1 [(5-1/2)(1.2 cm)/(2.5 cm)]

O = sin^-1 [2.4/2.5]

O = sin^-1 [0.96]

O = 75.5 degrees

Therefore, the angles at which the nodal lines are located are 75.5 degrees from the central line of the pattern. I hope this helps answer your question. Keep up the good work in your studies!

Best,