<p>A violinist puts her finger onto one of the strings of her violin, reducing its length but not changing the tension. Which of the following statements about the fundamental standing wave in the string is true?</p>
<p>According to Sparknotes, the correct answer is:</p>
<p>The frequency increases and the wavelength decreases. </p>
<p>I agree with the wavelength. However, I don't think so. Sparknotes sais:</p>
<p>The wave speed depends only on the type of string and the tension in the string; it does not change if the length changes</p>
<p>According to PR, this is wrong! They give the formula:</p>
<p>v= square<em>root(F</em>t/u)</p>
<p>where F_t is the tension and u is defined as: u = m/L</p>
<p>So, varying L will have an effect on v - right?
What's wrong?</p>
<p>The velocity doesn't change, and if we know the wavelength decreases, then to keep the same velocity, the frequency must increase.</p>
<p>The formula you give is one I haven't really seen before and I don't know if it's being used correctly in this context. I'd have to look into it, but odds are you won't need such a formula. </p>
<p>To solve that problem I would just know that the frequency increases (if you don't know through studying, think of past experience and intuition. Strings/etc tend to buzz a little faster when they are smaller as opposed to the larger string).</p>
<p>Well, your argumentation bases on the precondition that the velocity does not change. My formula sais: it does. I don't know whether it's such a special formula, but it obviously exists. I found it in PrincetonReview.</p>
<p>No, your formula says that m will change. If neither the medium or the tension change, the velocity will not change. The formula will not give you an answer without some context.</p>
<p>Thing is, the tension doesn't change but the string length does. Therefore, m must also change (mass of the string) because you are now considering a smaller portion of the string along with its respective shorter length. So both variables change, not just L. The velocity won't change since you're not changing certain things.</p>
<p>Ahhh, thanks. You are, of course, right. The variable u thus only denotes a specific property of the material, that is the string.
It's all clear, then :)</p>