Hi, I need help with another question!
A microwave transmitter emits waves towards a metal plate. The waves strike the plate and are reflected back along their path.
I really wish I could put the diagram here but I don't think that's possible... The diagram shows 5 nodes (TSRQP), where minima of intensity is observed. These points are 15 mm apart. What is the frequency of the microwave?
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Answer is 10GHz but I got 6.7GHz :C
What I did:
I assumed that frequency is for the 4th harmonic. So, I did: F=(2*15)/4.5
How do I do this?
wavelength=2(15mm)=.03m
freq=3E8/3E-2=10ghz
Thank you!!! :D
To determine the frequency of the microwave, you need to consider the distance between the nodes and the wavelength of the waves.
The distance between successive nodes (minima of intensity) is related to the wavelength of the waves by the following formula:
Distance between nodes = (n * λ) / 2
Where:
- Distance between nodes is the distance between successive minima of intensity, which is given as 15 mm in your case.
- n is the number of nodes between the two selected nodes (in your case, there are 5 nodes between the two selected nodes).
- λ is the wavelength of the waves.
From the formula, we can rearrange it to find the wavelength:
Wavelength (λ) = (2 * Distance between nodes) / n
Substituting the values into the formula:
Wavelength (λ) = (2 * 15 mm) / 5
Wavelength (λ) = 30 mm / 5
Wavelength (λ) = 6 mm
The frequency (f) of a wave is related to its wavelength (λ) by the equation:
Speed of light (c) = f * λ
Rearranging the equation to solve for the frequency:
Frequency (f) = c / λ
Now, if we assume the speed of light (c) is approximately 3 * 10^8 m/s, we can convert the wavelength to meters and calculate the frequency:
Frequency (f) = (3 * 10^8 m/s) / (6 mm * 10^-3 m/mm)
Frequency (f) = 5 * 10^10 Hz
Converting from Hz to GHz:
Frequency (f) = 5 * 10^4 GHz
Therefore, the frequency of the microwave is approximately 50 GHz, not 10 GHz or 6.7 GHz.
Please recheck your calculations to ensure accuracy. If you have any further questions or need additional assistance, please let me know!
To determine the frequency of the microwave, we need to analyze the standing waves created by the reflected waves on the metal plate. The standing waves exhibit nodes where the intensity is minimized. In this case, you mentioned there are 5 nodes (TSRQP) observed at points that are 15 mm apart.
One way to approach this problem is to consider the distance between adjacent nodes. In a standing wave, the distance between two adjacent nodes (e.g., T and S) corresponds to half a wavelength (λ/2) of the wave.
So, in this case, the distance between T and S is 15 mm. Since this is λ/2, we can find the wavelength (λ) by multiplying this distance by 2.
λ = 2 * 15 mm = 30 mm
Now, to find the frequency (f), we can use the formula:
v = f * λ
where v is the velocity of the wave. For electromagnetic waves, including microwaves, the velocity is the speed of light (c) which is approximately 3 * 10^8 m/s.
Converting the wavelength from mm to meters:
λ = 30 mm = 30 * 10^(-3) m = 0.03 m
Plugging this into the formula:
3 * 10^8 m/s = f * 0.03 m
Rearranging the equation to solve for frequency:
f = (3 * 10^8 m/s) / 0.03 m = 10^10 Hz = 10 GHz
So, the frequency of the microwave is indeed 10 GHz, not 6.7 GHz as you initially calculated.