What Is the Wavelength of the Signal Based on Goniometer Measurements?

AI Thread Summary
The discussion revolves around calculating the wavelength of a signal based on goniometer measurements. Initially, the receiver is positioned at 8.4 cm and later moved to 27.3 cm after passing through 10 minima and stopping at a maximum. The mistake in the initial calculation was not accounting for the fact that moving through 10 minima also includes 5 complete wavelengths. The correct formula for wavelength is derived as λ = (27.3 - 8.4) cm / 5, leading to a more accurate result. Understanding the relationship between minima and maxima is crucial for solving this problem correctly.
Mnemonic
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Homework Statement


Initially your receiver is positioned at a distance of 8.4 cm from the goniometer and recording a maximum intensity. You move it through 10 minimums in the intensity and then stop at the next maximum intensity. The receiver is now a distance of 27.3 cm from the goniometer.

What is the wavelength of the signal you have measured?

Homework Equations


ƛ/2=Distance between two maximums

The Attempt at a Solution


ƛ=2(27.3-8.4)cm
=37.8cm

It's that simple right?
I keep getting the wrong answer with this. What am I missing?
 
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Mnemonic said:

Homework Statement


Initially your receiver is positioned at a distance of 8.4 cm from the goniometer and recording a maximum intensity. You move it through 10 minimums in the intensity and then stop at the next maximum intensity. The receiver is now a distance of 27.3 cm from the goniometer.

What is the wavelength of the signal you have measured?

Homework Equations


ƛ/2=Distance between two maximums

The Attempt at a Solution


ƛ=2(27.3-8.4)cm
=37.8cm

It's that simple right?
I keep getting the wrong answer with this. What am I missing?
You are not taking into account that it was moved through many minima and maxima. You have calculated as though it was moved to the very next maximum.
 
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haruspex said:
You are not taking into account that it was moved through many minima and maxima. You have calculated as though it was moved to the very next maximum.

The wording in the question confused me. So you are saying that between each of the 10 minimums there was a maximum as well?
 
Mnemonic said:
The wording in the question confused me. So you are saying that between each of the 10 minimums there was a maximum as well?
That's the usual arrangement.
 
haruspex said:
That's the usual arrangement.

SO there are 5 complete wavelengths.

Therefore ƛ=(27.3-8.4)/5 cm
 
Mnemonic said:
SO there are 5 complete wavelengths.

Therefore ƛ=(27.3-8.4)/5 cm
That looks better.
 
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