question 48 in test 1 of sparknote physics

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1

<p>I was taking test in Sparknotes and I got this question, im so confused with the given answer, i think that linear mass density is equal m/L, when violinist reduce L -> mass density will increase, thus v decrease because v inversely proportional to linear mass density. Therefore, f decrease because both v and L decrease according to f=nv/2L
Also when reduce L, wavelength decrease according to the equation wavelength= L/n</p>

<p>so both f and wavelength decrease, but the right answer is A. f increase and wavelength decrease</p>

2

<p>The violinist doesn't / can't change the linear mass density, which you can think of as the thickness of the string. The linear mass density is the mass of the whole string divided by the length of the whole string.</p>

<p>So, v stays the same. When L is reduced, the fundamental wavelength has to fit in a smaller length, so the wavelength goes down. Since v = wavelength * frequency, the frequency must go up.</p>