Goniometers and Standing Waves

In summary: Did you get the same answer as before? In summary, the wavelength of the signal measured is 37.8 cm, taking into account the distance between each maximum and minimum. However, since there were 10 minimums and 5 complete wavelengths, the correct calculation is ƛ=(27.3-8.4)/5 cm, resulting in a wavelength of 3.78 cm.
  • #1
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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  • #2
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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  • #3
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?
 
  • #4
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.
 
  • #5
haruspex said:
That's the usual arrangement.

SO there are 5 complete wavelengths.

Therefore ƛ=(27.3-8.4)/5 cm
 
  • #6
Mnemonic said:
SO there are 5 complete wavelengths.

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

1. What is a goniometer and how is it used in science?

A goniometer is a scientific instrument used to measure angles. It typically consists of a circular scale with a protractor, a rotating arm with a pointer, and a stationary arm. It is commonly used in fields such as crystallography, physics, and engineering to accurately measure and record angles in various experiments and observations.

2. How does a goniometer work to measure angles?

A goniometer works by placing the object whose angle needs to be measured between the stationary arm and the rotating arm. The rotating arm is then moved until the pointer aligns with the object's edges or planes. The angle can then be read off the circular scale, which is typically calibrated in degrees or radians.

3. What are standing waves and how are they related to goniometers?

Standing waves are a type of wave that appears to be stationary, with no net movement of energy. They are formed when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. Goniometers are often used to measure the angles of these standing waves in experiments, particularly in the study of acoustics and vibrations.

4. How can goniometers be used to study crystal structures?

In crystallography, goniometers are used to accurately measure the angles between crystal faces. By rotating the crystal and measuring the angles with a goniometer, scientists can determine the crystal's lattice structure and identify the types of atoms present in the crystal.

5. Are there different types of goniometers and what are their uses?

Yes, there are several types of goniometers, each with a specific use in different fields of science. Some common types include the optical goniometer, used in mineralogy and crystallography, the X-ray goniometer used in X-ray crystallography, and the universal goniometer, which can measure angles in multiple planes. In addition, digital goniometers are becoming increasingly popular due to their accuracy and ease of use.

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