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, ... 2L/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.