TUTORIAL ANSWERS 230-235

 

 
 

Your Answer to Q230.  The answer is 1 s. If you did not get this correct, think about what the repeat time depends on.

Help: Fundamentals of Sound, Secs. 7-B, 7-D.

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The correct solution is here .

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Hint for Question 230: What is the smallest time that all modes will be back to their starting shapes. What is the frequency of the fundamental?
 
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Your Answer to 230. Congratulations, your answer is correct.

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Correct Answer to Question 230:  The frequency of the fundamental is 1 Hz, because the fourth harmonic is four times the frequency of the fundamental. The repeat time is then 1 s, that is, the period of the fundamental. It takes this long for the fundamental to repeat for the first time; meanwhile the fourth harmonic has repeated four times and is also back to its starting shape, so the entire wave now starts repeating.

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Your Answer to Q232.  Sorry, your answer is not correct. A wave is symmetric if the right side (the part to the right of a vertical line through the middle of the wave) is the mirror image of the left side. It is antisymmetric if the right side is the negative of the mirror image of the left side.

Help: Fundamentals of Sound, Sec. 7-B.

Or would you like a HINT?

You should try to work out the answer on your own, but if you insist on reading it the correct answer is here.

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Hint for Question 232:  Another way to judge symmetry is to consider the midline to be a hinge. Swing the left side over to the right. If it corresponds to the right side, the wave is symmetric; if you have to flip it around the horizontal as well (that is, make it the negative of what it was), it is antisymmetric.
 
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Your Answer to Question 232. Congratulations, your answer is correct.

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Correct Answer to Question 232:  This wave is antisymmetric. A way to judge symmetry is to consider the line vertically down the center to be a hinge. Swing the left side over to the right. If it then corresponds to the right side, the wave is symmetric; if you have to flip it around the horizontal as well (that is, make it the negative of what it was), it is antisymmetric. You have to make this extra flip in this case; the right side has the opposite sign as the left side.

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Your Answer to Q233.  Sorry, your answer is not correct.  An antisymmetric wave has only antisymmetric harmonics making it up.

Help: Fundamentals of Sound, Secs. 7-B, 7-D.

Or would you like a HINT?

You should try to work out the answer on your own, but if you insist on reading it the correct answer is here .

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Hint for Question 233:  An antisymmetric wave has only antisymmetric harmonics making it up. The antisymmetric harmonics are the even harmonics.
 
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Your Answer to Q233. Congratulations, your answer is correct.

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Correct Answer to Question 233:  b) is correct. An antisymmetric wave has only antisymmetric harmonics making it up. The antisymmetric harmonics are the even harmonics. Thus this wave is made up of the second, fourth, sixth, etc. harmonics. The second harmonic acts like a fundamental ("effective fundamental") for all the other even harmonics, that is, the fourth is two times the second, the sixth is three times the second, etc. The shortest time that all components are all back at their starting shapes is the period of the second harmonic, that is 1/(2 f0). The second harmonic frequency is the largest common factor of the other frequencies.

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Your Answer to Q235.  Sorry, your answer is not correct.  The repeat time is determined by the frequency spectrum. You need to understand the rules for finding the repeat time.

Help: Fundamentals of Sound, Secs. 7-B, 7-D.

Or would you like a HINT?

You should try to work out the answer on your own, but if you insist on reading it the correct answer is here .

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Hint for Question 235:  What is the slowest harmonic to return to its starting shape? The period of this may determine the repeat time (it does not always, however).
 
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Your Answer to Q235 . Congratulations, your answer is correct.

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Correct Answer to Question 235:  The correct answer is e). All three waves contain the fundamental. Thus after the period of the fundamental, all the harmonics in all three waves will have repeated an integral number of times, once for the fundamental, two times for the second harmonic, etc. This is the shortest time that all the components of every wave will be back to their starting shapes, so T0 = 1/f0 is the repeat time in all three cases. In each case it is 1/10 s.

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