cjh (11/22/82)
#N:harpo:19300003:000:2426
harpo!cjh Nov 22 10:16:00 1982
I would like to thank again everyone who has responded to my
"simple physics problem." It seems that the answer everyone here
gave is 25Hz. I'm glad, because that is what I got for an answer.
Here is one responce that I got from Richard Piner.
Carl,
The answer to the question is 25 Hz.
Your question does not specify if one end of the string is free
to vibrate or not. If it is not, the frequencies given are impossible.
So I assume that one end is free to vibrate. I will give solutions for
both cases, so you can see why I assume one end is free.
If both ends are fixed, there must be a node at each end, so the
series of possible wavelengths (l=wavelength) is,
(1/2)l (2/2)l (3/2)l (4/2)l.. .. (n/2)l
If one end is free, there must be a node at one end, and an
anti-node at the other end. Hence the possible wavelengths are,
(1/4)l (3/4)l (5/4)l (7/4)l.. ..([2n-1]/4)l
It can be shown that these wavelengths lead to the frequencies below:
both ends fixed one end free
--------------- ------------------
n f = 75 ? (2n -1)f = 75 ? n=1,2,3,4....
(n+1)f = 125 ? (2[n+1] -1)f = 125 ?
(n+2)f = 175 ? (2[n+2] -1)f = 175 ?
If we solve these we find f=50 in the first case and f=25 in the
second case. BUT when n=1, f=25 is the only value which fits the
equation. So the values given are only valid for the case of a
string with one end free to vibrate and one end fixed. You will note
that this problem can be solved with only two of the three frequency
values given, since you where told they are next to each other in
the series. As a side note,it is obvious that the answer is 25, since
the given series has two differences of 50, and the last positive number
in the series is 25. Hope this helps, and you can forward this answer to
the net if you want.
Richard Piner
Physics Dept.
Purdue University
West Lafayette, IN 47907
My instructor gave us an answer of 50Hz. He said that you cannot tell
from the information given if the string is open on one end or closed
on both and since the three frequencies are successive then the
series must be as in the first case above. He then solved n = 1.5
at 75Hz, f = 50. In class I normally would have let it pass, not
being normally a vocal student, but I
had always thought that 'n' had to be an integer. Are there exceptions
to this?
Thanks again;
Carl Hoffmann
harpo!cjh