Solving 2D Wave Interference - Find Wavelength & Speed

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SUMMARY

This discussion focuses on solving problems related to 2D wave interference, specifically calculating wavelength and wave speed. The first problem involves two point sources 5.0 cm apart, operating at a frequency of 6.0 Hz, with nodal lines crossing a metre stick at 35.0 cm and 55.0 cm. The relevant formula used is X/L=(n-1/2)λ/d. The second problem features two speakers 5 m apart radiating sound at a wavelength of 2.00 m, with sound propagating at 338 m/s. The user seeks assistance in determining the distances from a nodal point to the speakers.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with the formula X/L=(n-1/2)λ/d
  • Knowledge of frequency and wavelength relationships
  • Basic concepts of sound propagation in air
NEXT STEPS
  • Study the derivation and application of the wave interference formula X/L=(n-1/2)λ/d
  • Learn about the relationship between frequency, wavelength, and wave speed in various mediums
  • Explore the concept of nodal and antinodal points in wave interference
  • Investigate practical applications of 2D wave interference in acoustics and optics
USEFUL FOR

Students and educators in physics, particularly those focusing on wave mechanics, as well as audio engineers and anyone interested in the principles of sound wave interference.

F.B
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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.
 
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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.
 

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