How many nodal and antinodal lines are there?

In summary, the conversation discusses an interference pattern produced by two point sources separated by 3.5cm and vibrating in phase. The first order nodal line forms an angle of 20 degrees with the perpendicular bisector of the line segment joining the two sources. The wavelength is calculated to be 2.4cm, and the number of nodal and antinodal lines is up to first order antinodal and up to 2nd order nodal. The nodal lines occur at path differences of 0.5λ, 1.5λ, 2.5λ, etc., and their relationship with the source separation is questioned.
  • #1
Ilan
2
0

Homework Statement


In an interference pattern produced by two point sources separated by 3.5cm and vibrating in phase, the first order nodal line forms an angle of 20 degrees with the perpendicular bisector of the line segment joining the two sources. What is the wavelength? How many nodal and antinodal lines are there?


Homework Equations


PD = m * lambda
PD = d * sin(theta)

The Attempt at a Solution


3.5sin20=0.5lambda
lambda = 2.4cm

I'm not sure how to go about calculating the number of lines. The answer is up to first order antinodal and up to 2nd order nodal.
 
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  • #2
Ilan said:

Homework Statement


In an interference pattern produced by two point sources separated by 3.5cm and vibrating in phase, the first order nodal line forms an angle of 20 degrees with the perpendicular bisector of the line segment joining the two sources. What is the wavelength? How many nodal and antinodal lines are there?


Homework Equations


PD = m * lambda
PD = d * sin(theta)

The Attempt at a Solution


3.5sin20=0.5lambda
lambda = 2.4cm

I'm not sure how to go about calculating the number of lines. The answer is up to first order antinodal and up to 2nd order nodal.

Nodal lines occur in places where the path difference from the sources is 0.5λ, 1.5λ, 2.5λ, ...

If your wavelength of 2.4cm is correct, that means 1.2cm, 3.6cm, 6.0cm , etc .

How do those differences fit alongside a source separation of 3.5 cm ?

Note: I have not checked, at all, the correctness of your λ = 2.4cm answer
 

1. How can I determine the number of nodal and antinodal lines in a wave?

The number of nodal and antinodal lines in a wave can be determined by the frequency of the wave. A higher frequency will result in more nodal and antinodal lines, while a lower frequency will result in fewer lines. Additionally, the type of wave (transverse or longitudinal) can also affect the number of lines.

2. What is the difference between a nodal line and an antinodal line?

A nodal line is a point on a wave where there is no displacement from the resting position. In other words, the wave does not move at this point. An antinodal line, on the other hand, is a point where the wave has maximum displacement from the resting position. This means that the wave is moving the most at this point.

3. Can the number of nodal and antinodal lines change?

Yes, the number of nodal and antinodal lines can change depending on the frequency and type of wave. For example, if the frequency of a wave increases, the number of nodal and antinodal lines will also increase.

4. How do nodal and antinodal lines affect the behavior of a wave?

Nodal and antinodal lines can affect the behavior of a wave by determining its amplitude (height) and wavelength (distance between two consecutive peaks or troughs). They also play a role in interference patterns and standing waves.

5. Are there any real-world applications of nodal and antinodal lines?

Yes, nodal and antinodal lines are important in various fields such as music, acoustics, and optics. In music, they determine the pitch and timbre of a sound. In acoustics, they are used to study sound waves and their behavior. In optics, they play a role in understanding the properties of light and its interactions with matter.

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