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A lowpass Butterworth filter has a corner frequency of 1 kHz and a roll-off of 24 dB per octave in the stopband. If the output amplitude of a 3-kHz sine wave is 0.10 V, what will be the output amplitude of a 20-kHz sine wave if the input amplitudes are the same
The Butterworth filter is a type of electronic filter that has a flat frequency response in the passband and falls off at a rate of -6 dB per octave in the stopband. The filter's output amplitude depends on the input amplitude of the signal and the filter's corner frequency.
1 kHz is the corner frequency of the lowpass Butterworth filter with a roll-off of 24 dB per octave in the stopband. When a 3 kHz sine wave is input into the filter and its output amplitude is 0.10 V, the output amplitude of a 20 kHz sine wave if the input amplitudes are the same is calculated as follows:To begin, we must determine the filter's attenuation rate at the output frequency, which is 20 kHz.
The stopband attenuation rate is 24 dB per octave, which means that the filter's attenuation increases by a factor of 2 for every octave increase in frequency beyond the corner frequency. As a result, at 2 kHz, the filter's attenuation will be 24 dB, and at 4 kHz, it will be 48 dB.
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calculate the maximum internal crack length allowable for a 2024-t3 al alloy used as a structural component in a commercial airliner. during service, this component is subjected to a tensile stress of 675 mpa. assume a value of 1.2 for y.
To calculate the maximum internal crack length allowable for a 2024-T3 Al alloy used as a structural component in a commercial airliner, we can use the fracture mechanics concept.
Fracture mechanics involves the use of stress intensity factor (K) to determine the critical crack length (a) for a given material and stress condition. The stress intensity factor can be calculated using the following equation:
K = Y * σ * sqrt(π * a)
Where:
- Y is the geometric factor (given as 1.2)
- σ is the tensile stress applied (given as 675 MPa)
- a is the crack length (unknown)
To find the maximum crack length allowable, we need to rearrange the equation and solve for a:
a = (K / (Y * σ * sqrt(π)))
Now, we can substitute the given values into the equation:
a = (K / (1.2 * 675 * sqrt(π)))
It's important to note that we need to know the specific value of the stress intensity factor (K) for the 2024-T3 Al alloy to obtain an accurate result. This value is typically determined through testing or can be obtained from material property databases.
Without knowing the value of K, we cannot calculate the maximum internal crack length allowable for the given alloy and stress condition.
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