Solving 2D Wave Interference - Find Wavelength & Speed

[F.B]

I just learned interference of waves in two dimensions, and i don't really understand it. Well i know how to use the formula and everything but i don't know what I am given in the questions. So can you help me with my given.

1. Two point sources, 5.0 cm apart, are operating in phase, with a common frequency of 6.0 hz, in a ripple tank. A metres stick is placed above the water, parallel to the line joining the sources. The first nodal lines (the ones adjacent to the central axis) cross the metre stick at the 35.0 cm and 55.0 cm marks. Each of the line joining the two sources. Determine the wavelength and speed of the waves.

I know i have to use this formula:

X/L=(n-1/2)lamda/d

i know that:
n=1
f=6
d=5
But i don't know what the rest of the numbers are.

My second questions.

Two very small, identical speakers, each radiating sound uniformly in all directions, are placed at points S1 and S2. The speaks are 5 m apart and are connected to an audio source so that they radiate in phase, at a common wavelength at 2.00 m. Sound propogates in air at 338 m/s
a) Point M, a nodal point is 7.0 m from S1 and more than 7 from S2. Find 3 possible distances M could be from S2.

I know that i am given:
d=5m
MS1=7
MS2= x+7
lamda=2m

I don't know what n is so i don't know how to solve this question so can anyone please help me with both these questions.

 

[Astronuc]

Think of the sound waves as concentric rings spreading outward both each source. Allow the radii of the rings to correspond to integral numbers of wavelength (because they are in phase), and see where they intersect.

The node lines are where the peaks of the wave sets intersect.

 

[quicknote]

Hello, it's great that you are learning about 2D wave interference. I can definitely help you with your given questions.

For the first question, you are correct in using the formula X/L=(n-1/2)lamda/d. In this case, X is the distance between the first nodal lines (35.0 cm and 55.0 cm), L is the distance between the two point sources (5.0 cm), n is the number of nodal lines (1), and d is the distance between the two sources (5.0 cm). From this, we can solve for the wavelength (lamda) and speed (v) using the following equations:

Wavelength (lamda) = (2X/n)(d/L)
Speed (v) = lamda*f

Substituting the given values, we get:

Wavelength (lamda) = (2*45 cm/1)(5 cm/5 cm) = 90 cm
Speed (v) = (90 cm)(6.0 Hz) = 540 cm/s

For the second question, we can use the same formula X/L=(n-1/2)lamda/d. In this case, X is the distance between the two speakers (5 m), L is the wavelength (2.00 m), n is the number of nodal lines (1), and d is the distance between the two speakers (5 m). We can solve for the distance between point M and speaker S2 (MS2) using the following equation:

MS2 = X - MS1 = 5 m - 7 m = -2 m

Since the distance between point M and speaker S2 must be greater than 7 m, we can have three possible distances for M:

1. MS2 = 7 m + 2 m = 9 m
2. MS2 = 7 m + 5 m = 12 m
3. MS2 = 7 m + 8 m = 15 m

I hope this helps you understand the questions better. Keep up the good work in your studies!