**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.

Would you like a **HINT**?

The correct solution is here .

Return to Question 230.

**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?

Return to Question 230.

**Your
Answer to 230. **Congratulations, your answer is **correct**.

If you would like, you can compare your answer to the "official" correct answer .

Return to Question 230.

**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.

Return to Question 230.

**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.

Return to Question 232.

**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.

Return to Question 232.

**Your
Answer to Question 232. **Congratulations, your answer is **correct**.

If you would like, you can compare your answer to the "official" correct answer .

Return to Question 232.

**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.

Return to Question 232.

**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** .

Return to Question 233.

**Hint
for Question 233:** An antisymmetric wave has only antisymmetric harmonics
making it up. The antisymmetric harmonics are the even harmonics.

Return to Question 233.

**Your
Answer to Q233. **Congratulations, your answer is **correct**.

If you would like, you can compare your answer to the "official" correct answer .

Return to Question 233.

**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 *f*_{0}). The second harmonic frequency is the **largest
common factor** of the other frequencies.

Return to Question 233.

**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** .

Return to Question 235.

**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).

Return to Question 235.

**Your
Answer to Q235 . **Congratulations, your answer is **correct**.

If you would like, you can compare your answer to the "official" correct answer .

Return to Question 235.

**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 *T*_{0} = 1/*f*_{0} is the repeat time in all three cases. In each case
it is 1/10 s.

Return to Question 235.

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