TBR sound phase I passage 1

[deleted783484]

Passage says " The 4 strings of a violin all have the same length of roughly 12 inches. in an experiment students studied the 4 strings of an old violin and the four strings produced these frequencies

string I : 196 Hz
string II: 294Hz
string III: 440 Hz
string IV: 659 Hz

The question asks " The wavelength of a standing wave on each string is "
A. 0.326m for all strings
B. 0.652m for all strings
C. 1.73m 1.16m 0.77m 0.52m for strings I through IV
D. 3.46m 2.32m 1.54m 1.04m for strings I through IV

Answer is B and explanation says The fundamental wave is associated with the fundamental frequency of the string. There are no nodes between the endpoints of the string in the fundamental node so the string is half a wavelength long.

I don't understand this? why did they use the fundamental wave ?

Thanks!

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[BerkReviewTeach]

Whenever someone posts a question from our books, I like to look it up and get a bearing on the context. This question seems familiar (I know I answered it in office hours at some junction but can;t recall when), but I cannot find it in any of the recent editions of our physics books. I'm not sure why it was removed from the book (or when it was removed), but apparently it was deemed unfit for the recent editions. Nevertheless, lets consider what the question is getting at.

It's a "bait-and-switch" style question where you are given excess extraneous information. While the frequency produced by a string depends on its length, tension, mass per length, and harmonic, the wavelength only depends on the harmonic and the length of the string. The string is said to be 12 inches long, which amounts to a little less than one-third of a meter. The standing wave can be associated with a specific harmonic but the most abundant one is typically the first harmonic, or fundamental wave. For the fundamental wave (with nodes at each end of the string and an antinode in the middle), the wavelength is twice the length of the string. This makes the best answer a little less than two-thirds of a meter (choice B).

In the context of the question and answer choices, you should have eliminated choices C and D, because all four strings have the same length, so they should have the same standing wave wavelength. Choice A would be true if they were asking for the second harmonic, but they did not specify any harmonic. So given the answer choices they gave, the best fit is to take the simplest case, which is the first harmonic (fundamental frequency). Choice B is the best of the four choices.

 

[deleted783484]

Whenever someone posts a question from our books, I like to look it up and get a bearing on the context. This question seems familiar (I know I answered it in office hours at some junction but can;t recall when), but I cannot find it in any of the recent editions of our physics books. I'm not sure why it was removed from the book (or when it was removed), but apparently it was deemed unfit for the recent editions. Nevertheless, lets consider what the question is getting at.

It's a "bait-and-switch" style question where you are given excess extraneous information. While the frequency produced by a string depends on its length, tension, mass per length, and harmonic, the wavelength only depends on the harmonic and the length of the string. The string is said to be 12 inches long, which amounts to a little less than one-third of a meter. The standing wave can be associated with a specific harmonic but the most abundant one is typically the first harmonic, or fundamental wave. For the fundamental wave (with nodes at each end of the string and an antinode in the middle), the wavelength is twice the length of the string. This makes the best answer a little less than two-thirds of a meter (choice B).

In the context of the question and answer choices, you should have eliminated choices C and D, because all four strings have the same length, so they should have the same standing wave wavelength. Choice A would be true if they were asking for the second harmonic, but they did not specify any harmonic. So given the answer choices they gave, the best fit is to take the simplest case, which is the first harmonic (fundamental frequency). Choice B is the best of the four choices.

Thank you!!