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lys-0071 [83]
4 years ago
6

A sinewave has a period (duration of one cycle) of 6.5ms. What is its corresponding frequency expressed to 3 significant figures

? If the frequency of this sinewave is increased by a factor of 3, calculate the new period value, expressing your answer again to 3 significant figures. Clearly show all your working.
Computers and Technology
1 answer:
Sergio [31]4 years ago
8 0

Answer:

(A) Corresponding frequency = 154 Hz (in 3 significant figures)

(B) New Period = 0.00217 s (in 3 significant figures)

Explanation:

The given information is as follows:

The period of a sinewave =  T = 6.5\ ms = 6.5\ * \ 10^{-3}\ s = 0.0065s

<u>Part-A</u>

Corresponding frequency f is required.

Since,

frequency = \frac{1}{Period} \\f = \frac{1}{T}

Plug the value of the period, T, of a given sine wave in the above equation:

f = \frac{1}{0.0065} \\f= 153.846\ Hz

The aforementioned frequency should be expressed to 3 significant figures (which is the requirement of the question). So, take the first three digits of the answer (since they are significant), but as you can see after the decimal point, the digit is greater than 5, round the third digit off to 4. Hence, the corresponding frequency would be 154 Hz (expressed in 3 significant figures).

<u>Part-B</u>

The frequency of the sinewave is increased by a factor of 3. It means that you need to multiply the frequency found in the Part-A by 3.

Hence, the new frequency will be as follows:

f_{new} = 3*f_{old} \\f_{new} = 3*153.846\\f_{new}= 461.538\ Hz

Note that for finding the new frequency, the old, unrounded off frequency is used.

Since,

New\ frequency = \frac{1}{New Period} \\f_{new} = \frac{1}{T_{new}}\\T_{new} = \frac{1}{f_{new}}

Plug the value of the new frequency in the above equation, and evaluate for the new period:

T_{new} = \frac{1}{461.538}}\\T_{new} = 0.00216667\ s

Again, round it off to three significant figures. Zeroes before 2 do not matter when we count for the significant figures (a significant figure rule). Also make sure to round off the third digit from 2 (since the digit next to that digit is greater than 5).

Hence, the new period value will be 0.00217s (expressed in 3 significant figures).

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Answer:Analysis is derived from the Greek word ‘analusis’, which translates into ‘breaking up’ in English. Analysis is older than the times of great philosophers like Aristotle and Plato. As discussed in the previous section, analysis is the process of breaking down a big single entity into multiple fragments. It is a deduction where a bigger concept is broken down to smaller ones. This breaking down into smaller fragments is necessary for improved understanding.

So, how does analysis help in design thinking? During analysis, design thinkers are required to break down the problem statement into smaller parts and study each one of them separately. The different smaller components of the problem statement are to be solved one-by-one, if possible. Then, solutions are thought for each of the small problems. Brainstorming is done over each of the solutions.

Later, a feasibility check is done to include the feasible and viable solutions. The solutions that don’t stand firm on the grounds of feasibility and viability are excluded from the set of solutions to be considered.

Design thinkers are, then, encouraged to connect with the diverse ideas and examine the way each idea was composed. This process of breaking down the bigger problem statement at hand into multiple smaller problem statements and examining each as a separate entity is called analysis.

Reductionism

The underlying assumption in analysis is reductionism. Reductionism states that the reality around us can be reduced down to invisible parts. The embodiment of this principle is found in basic axioms of analytic geometry, which says “the whole is equal to the sum of its parts”. However, understanding of a system cannot be developed by analysis alone. Hence, synthesis is required following analysis.

Synthesis

Synthesis refers to the process of combining the fragmented parts into an aggregated whole. It is an activity that is done at the end of the scientific or creative inquiry. This process leads to creation of a coherent bigger entity, which is something new and fresh. How does synthesis come into picture in design thinking?

Once the design thinkers have excluded the non-feasible and non-viable solutions and have zeroed-in on the set of feasible and viable solutions, it is time for the thinkers to put together their solutions.

Out of 10 available solutions, around 2-3 solutions may need to be excluded since they may not fit into the larger picture, i.e. the actual solution. This is where synthesis helps.

The design thinkers start from a big entity called the problem statement and then end up with another bigger entity, i.e. the solution. The solution is completely different from the problem statement. During synthesis, it is ensured that the different ideas are in sync with each other and do not lead to conflicts.

Analysis + Synthesis = Design Thinking

Analysis and synthesis, thus, form the two fundamental tasks to be done in design thinking. Design thinking process starts with reductionism, where the problem statement is broken down into smaller fragments. Each fragment is brainstormed over by the team of thinkers, and the different smaller solutions are then put together to form a coherent final solution. Let us take a look at an example.

Analysis Synthesis

Case Study

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Analysis − Now, let’s break down the problem statement into various constituent parts. Following are the subparts of the same problem statement, broken down to elementary levels.

The employees are not motivated anymore to work in the company.

Appraisal cycle has something to do with attrition.

Knowledge transfer is necessary for new employees.

Knowledge transfer adds to the cost of the company.

Synthesis − Now, let's start solving each problem individually. In this step, we will do synthesis. Let's look at one problem at a time and try to find a solution only for that problem statement, without thinking of other problem statements.

Explanation:

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Answer:

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Explanation:

When we convert any decimal number into the hexadecimal number we have to divide that number with 16.

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Now to convert this in hexadecimal divide it with 16.

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