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Given y = A sin(2000t - (pi/16)x), calculate wavelength, frequency, and speed of the wave.
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Step-by-step solution
4 stepsThe given equation for a plane progressive wave is:
This equation is in the standard form , where:
- is the amplitude
- is the angular frequency
- is the wave number
From the given equation, we can identify:
Angular frequency, rad/s
Wave number, rad/m
Now, let's calculate the required quantities.
Calculate the wavelength ().
The wave number is related to the wavelength by the formula .
Rearranging for :Substitute the value of :
The wavelength is .
Calculate the frequency ().
The angular frequency is related to the frequency by the formula .
Rearranging for :Substitute the value of :
Using :
The frequency is .
Calculate the speed () of the wave.
The speed of the wave can be calculated using the formula .
Substitute the values of and :Using :
The speed of the wave is .
Calculate the period () of the wave.
The period is the reciprocal of the frequency :
Substitute the exact value of :
Using :
The period is .
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