**TUTORIAL
ANSWERS 175-180**

**Your
answer to Q175: **Sorry,
your answer is **not **correct. To be in resonance a tone must have
the same frequency as one of the resonant frequencies of the string. You may
have realized that and still gotten the answer wrong, because it is actually
a tricky question.

Help: *Fundamentals of
Sound*, Chap. 4.

Or, would you like a HINT?

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

Return to Question
175.

**Hint
for Q175**: Think of a possible set of normal modes of a string
that has 4 Hz and 2 Hz as allowed modes. Is that the only possible set??? Also
what is it that tells you the possible wavelengths on the string?

Return to Question 175

**Your
answer to Q175: **Congratulations, your answer is **correct**!

To read the "official" correct answer, click HERE.

Return to Question
175.

**Correct
answer to Q175**: It is clear that 1 Hz is **not** one of the
resonant frequencies of the string since that tone does not excite the string.
One possibility is that 2 Hz is the LNRF of the string. That would fit the data
that the 2 Hz and 4 Hz tones cause it to vibrate. However, there are other possibilities:
suppose that the lowest mode is 2/3 Hz. (The lowest mode does not have to be
an integer number of Hertz!) Then 2 Hz = 3(2/3) Hz and 4 Hz = 12(2/3) Hz would
still be resonant frequencies and those tones would then excite the string.
We are unable to tell from the information given what the LNRF is. We have no
information on the wave velocity either. However, from the information that
the string is 1 ft long we know all the wavelengths possible; they are 2 ft,
1 ft, 2/3 ft, ... 2*L/n* where *n* is 1,2,3... So c) is the
answer.

Return to Question
175.

**Your
answer to Q180: **Sorry, your answer is **not **correct. To
be in resonance, a tone must have the same frequency as one of the standing
waves on the string. You might read the answer to Question
175.

Help: *Fundamentals of
Sound*, Chap. 4.

Or, would you like a HINT?

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

Return to Question
180.

**Hint
for Q180**: See the answer to Question 175.

Return to Question 180

**Your
answer to Q180: **Congratulations, your answer is **correct**!

To read the "official" correct answer, click HERE.

Return
to Question 180.

**Correct
answer to Q180**: As in Question 175, we cannot tell if 9Hz is the LNRF
or not (4.5 Hz might be the LNRF, for example), but we certainly know that it
is one of the allowed modes of the string, otherwise it would not resonate.
We can also find the allowed wavelengths of standing waves on the string from
knowing its length as in Question 175. So ii and iv are correct, and the answer
is e).

Return
to Question 180.

ab_webmaster@abacon.com

©2002 William J. Mullin

Legal Notice