Find maximum wavelength using minimum wavelength and frequency difference

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To find the maximum wavelength given a frequency difference of 10 GHz and a minimum detected wavelength of 4910 µm, the relationship λƒ=c is essential. The minimum wavelength corresponds to the maximum frequency, which clarifies the approach to solving the problem. The initial attempt to convert the frequency difference to wavelength and add it to the minimum wavelength was incorrect. Understanding that the minimum wavelength relates to the maximum frequency was a key realization in resolving the confusion. This insight is crucial for accurately determining the maximum wavelength.
Shaulah
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Homework Statement


A radar receiver can be tuned to detect signals are different wavelengths. If the frequency difference between the minimum and maximum wavelength is 10 GHz and the minimum detected wavelength is 4910µm. What would be the maximum wavelength?

Homework Equations


λƒ=c

The Attempt at a Solution


I attempted to use the above equation to convert 10GHz to wavelength and then add to the minimum wavelength but this appears to be incorrect and I'm struggling to figure out the proper way to go about this. I know I must be missing something very basic
 
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Shaulah said:

Homework Statement


A radar receiver can be tuned to detect signals are different wavelengths. If the frequency difference between the minimum and maximum wavelength is 10 GHz and the minimum detected wavelength is 4910µm. What would be the maximum wavelength?

Homework Equations


λƒ=c

The Attempt at a Solution


I attempted to use the above equation to convert 10GHz to wavelength and then add to the minimum wavelength but this appears to be incorrect and I'm struggling to figure out the proper way to go about this. I know I must be missing something very basic
Does the minimum wavelength correspond to the minimum or to the maximum frequency ?
 
Ah! minimum wavelength corresponds to maximum frequency! Thank you! That little error was throwing quite the wrench into the problem
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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