a-string-fixed-at-both-ends-has-a-length-of-6-m-and-supports-a-standing-wave-with-a-total-of-4-nodes

Question

A string, fixed at both ends, has a length of 6 m and supports a standing wave with a total of 4 nodes. If a transverse wave can travel at 40 m/s down the rope, what is the frequency of this standing wave?
(A) 6.7 $\mathrm{Hz}$
(B) 10 $\mathrm{Hz}$
(C) 20 $\mathrm{Hz}$
(D) 26.7 $\mathrm{Hz}$

Guilherme Barros · Accepted Answer

it&#x27;s problem. We&#x27;re gonna talk about the frequency and wavelength off waves. Eso consider that we have string like this one shown in the picture we call nodes. These points of minimum amplitude here that I&#x27;m marking in rep. Okay, so if this is a standing wave, these points we&#x27;ll always have zero amplitude and the distance between, uh, two nonconsecutive consecutive points, as shown here in the picture is equal to the wave one. Okay, so this year is one wavelength off the week. Yeah. Okay. Also, we know that the frequency times the wavelength is equal to the speed of replication of the waves. V In our problem, we have ah, string that has a length off 6 m and has four nodes. So the string would look something like this. Okay, so notice that there are four notes here. 1234 uh, in the length is equal to 6 m. And the exercise tells us that the speed of propagation of the waves is it which is 40 m per second. And our goal is to find what is the frequency of the weight. Now, notice that in this wave we have 1.5 wavelength because this year is one up wavelength. This here is half a wavelength. Eso lum the f I&#x27;m sorry. So one 0.5 times the wavelength is able to 6 m. So long Day six divided by 1.5. That&#x27;s 4 m. This is the This is the wavelength on the weight now F times Lunda is V so f is London video Very, very London. This means that F is equal to 40 m per second, divided by Lambda, which is 4 m. So AF is equal to 10 Hertz, which is our answer, disagrees with option B in the alternatives.

Donald Albin · Answer

So we have a one meter long string, so I&#x27;m going to write. L is 1.0 meters and we have successive frequencies at 24 36 Hertz. Well, we know that all of the frequencies are an integer multiple of the, um, fundamental frequency. So if we just take the 36 hurts minus 24 hurts. Since they are successive, that means that there are only one, um, fundamental frequency apart. So that would be 12 hurts. Yeah. The fundamental frequency is 12 hurts. So be Oh, no. We need to get the wave speed also, um, speed equals wavelength, times frequency. But I also know that the fundamental frequency is the speed over to l. Um, for new mental frequency is 12. Speed is what we&#x27;re solving for two times one, um, so making sure that so the speed is going to be just solving this for V 24 meters per second. Now we can move on to be so at 36 Hertz, we know that M is three. And so there will be three notes. And so if we draw the standing wave pattern, we just have to draw three nodes understanding that one of them is here. One of them is here. Excuse me. That is the third. No, this is not correct. Um, the number of nodes is the mode number plus one. And so, um, it&#x27;s the third modes. That means that there will be four nodes, nodes, All right. And now we can connect between the nodes.

Ze-Han Lee · Answer

So in this problem, we have a standing wave and ah, who? And it has four notes. So it would be like this. Careful notes. Right. So this is the one, 23 and four, right? And when l know Toland&#x27;s is Ah, six meters. And as you&#x27;re gonna come the period of this. Ah, the whole thing. You can say that. There&#x27;s, ah, 1.5 period. Okay, so the ah, the we see that the 1.5 times the wavelength equal to a total ends, which was six meters ray. So we blends is four meters okay?

Kai Chen · Answer

So in this question, where did it missed Any weeks? We have a string that is on next on bulk cents. String is 8.4 meters film and we also have a mess. It also the mess of 0.120 kilogram. Um and it&#x27;s subjected to attention of life. Only six you took so together these information go tell us what is the speed of trouble of this road Now this road is said us lady and we ask what, What? His speed of the wave on this dream. Um so we can solve it by visit the formulas that you closed How overview and mu the mass density is equal to end over out. So if we solve this equation, he sees this 96 new turn subsequent one to kill grand times. They put four meter and we take the square root of this just translate to be 82 meters per second And now Mr Kidd party in part B. The question asks, what is the longest possible wavelengths forest in Italy? Well, as long as possible with so the longest possible way dance is asking the standing wave with at least knows as possible. Eggs are studying one of the longest in with possible with the stream. And that happens when we have a standing wave like this. Almost slates are pinned up. So, uh, that is part B for the skinny with Alexis. Silence is the weapons is two types. So it&#x27;s, um, 16.8 meter, this in part C. We need to find the frequency of it where we knows us lead of travel. And we knows, uh, we know the way less of it. So we can divide some 82 meters per second. Offers 16.8 litre to figure out the frequency is 4.88 hertz.

Villiam Zelinsky · Answer

for part A. We&#x27;re trying to find the longest standing wave possible on a string. So the first thing we&#x27;ll need to know is the given value, which is that the length of the string is two years then using this given length meaning to get a formula for the problem The formula we use is Ling is equal to mass times wave ling divided by to Since we&#x27;re given that the length is two meters, we plug this in for L Now given the formula, we&#x27;ve plug in the numbers. Starting at M equals one tissue where we get the longest wavelengths for M equals one. If we solve this, the wavelength is equal to four for m equals to If we saw this the wavelength this to for M equals three we solve this The wavelength is 4/3 and for m equals four the way fling is one since from M equals one to m equals for the numbers decrease we solved for unknown which is the wave ling. So we get that the longest wavelengths is that m equals one for parts be were asked to find the lowest standing wave frequency So we know that the wave speed is 50 six meters her sick. So we&#x27;re looking for our unknowns, which is the wave frequency first since the longest wave Ling is that M equals one. The shortest is that M equals four. So the wavelength is equal 24 then just saw for the frequency we divide the speed by the wavelength or 56 divided by four to get the frequency so the frequency is 14 hurts.

Sarah Mccrumb · Answer

everybody is. So for this one, we need to determine the wavelength and what is fundamental frequency of the string. So we have a and it looks like the wave function is gonna look like this. We got this guy going on here, and then we have length of here. So because of this, um, and I didn&#x27;t do it correctly. How? We should let me, um, make this how it appears. So you guys can understand. What better? So we get, um, Landover two plus Landover two plus Landover Teoh. Um, plus Lambda over to so being, I need to get one Teoh. Well, I&#x27;m gonna try to get as good as it should be, So there we go. And, um, this is illegal to lambda. And so land, uh, is the eagles to the length divided by two, which is gonna be 60 times native, two meters. And we can say the, um the link is 1 20 centimeters equals 1 20 times 10 to negative two meters and B is asking us, um, if the position is B is asking us what is the fundamental frequency of the string. So we have because you want about a by frequency to equals in wine over in and four, my man. And four in and four. And from this we have frequency wide over 1 20 there. Which is this one here which is given to us, um, above. So because it says in the stream is 1 20 centimeters long stream. And that&#x27;s what we get this for. This here. And, um now, in one is will be equal to one in the city before. Okay, so I&#x27;m gonna solve frequency of once we get 1 20 divided by four. And this is going to give us 30 hertz. Okay. Thank you, guys.

Problem

A sound wave travels through a metal rod with wav…

Problem 6 Easy Difficulty

A string, fixed at both ends, has a length of 6 m and supports a standing wave with a total of 4 nodes. If a transverse wave can travel at 40 m/s down the rope, what is the frequency of this standing wave?
(A) 6.7 $\mathrm{Hz}$
(B) 10 $\mathrm{Hz}$
(C) 20 $\mathrm{Hz}$
(D) 26.7 $\mathrm{Hz}$

Answer

B

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