Finding the width of a diffraction slit

AI Thread Summary
To find the width of a diffraction slit that is seven times larger than the wavelength for various electromagnetic waves, the wavelength can be calculated using the formula λ = c/f, where c is the speed of light. For a radio wave at 100 MHz, the slit width would be 7 times the calculated wavelength. Similarly, for a 2.0 GHz cell phone signal, red light at 5e14 Hz, and X-rays at approximately 4e20 Hz, the same method applies. The initial confusion stems from misunderstanding the relationship between frequency and wavelength rather than the concept of diffraction itself. Understanding this relationship is crucial for solving the problem correctly.
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Homework Statement


Single-slit diffraction can be observed with any type of electromagnetic wave (not just light). Suppose you want to make a diffraction slit whose width is seven times larger than the wavelength for the following cases. How wide would the slit be?

(a) A radio wave for your favorite FM station (f = 100 MHz)


(b) The waves that carry your cell phone signals (f = 2.0 GHz)


(c) Red light (f = 5e14 Hz)


(d) The X-rays used in your dentist's office (f ≈ 4e20Hz)



Homework Equations





The Attempt at a Solution


I honestly have no idea where to begin with this.
I do know that the answer to a) is 7*3.. but I don't know why?
If anyone can point me in the right direction it would be appreciated.
 
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The relationship between frequency and wavelength is

\lambda=\frac{c}{f}

where c is the speed of light. The problem has nothing to do with diffraction.
 

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