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The rate of vibration of a string under constant tension variesinversely with the length of the string. If a string is 48 incheslong and vibrates 256 times per seco...

Question

The rate of vibration of a string under constant tension variesinversely with the length of the string. If a string is 48 incheslong and vibrates 256 times per second, what is the length of astring that vibrates 384 times per second?none of these32 inches72 inches24 inches

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 48 inches long and vibrates 256 times per second, what is the length of a string that vibrates 384 times per second? none of these 32 inches 72 inches 24 inches



Answers

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 48 inches long and vibrates 256 times per second, what is the length of a string that vibrates 576 times per second?

If the frequency vibration very is inversely with the length of the string. We have that relation and then times constant of proportionality. So we have initial conditions of frequency is equal to 200 56 hertz, and length is equal to 48 inches. Let's find out what K is 2 56 equals K over 48. So that means that K would be equal to 12,288. What is it? Like this string, it vibrates at a frequency of 576 hertz. So 5 76 is equal to 12,288 over l solving for L. We get that. L is equal to 21 points three inches.

Were given that the rate of a vibration of a string varies inversely with the length of the string. It was string is 48" long and vibrates 256 times per second. We need to find the length of the string when it vibrates 576 times per second. So we use the beginning information. So the rate of the vibration varies inversely with our legs. So our vibration is equal to K. Inversely with our length. So we'll call that al So we have if a string is 48" long and vibrates 256 times per minute. We can use that information to find our K. So we plug in our values so we have 256 is equal to K. Are unknown, Divided by 48. We cross multiply and we get 256 times 48. This comes out to be 12,288 is equal to K. So our equation becomes The vibration rate of vibration is equal to 1 12,288, divided by by um L So now we find the last part, it says the length of the string. So we gotta find L when it vibrates 567, times per second. So we have 576 is equal to 12,288 divided by L. We're gonna cross multiply So we get all times 576 is equal to 12,288. We divide both sides by 576. And we get That the string is approximately 21 and a third, which comes out to be 21.333 repeating inches long.

You a vibration Mystery varies inversely with the length of the strings. We have an equation here. V is equal to K divide by L. B being the velocity, the vibration rate of vibration of the string and l being the length of the string and caging a constant value that we had to find the number for the value of in order to create the equation to create that relationship. Ah, and to answer the question So we're told that the string is 24 inches long, so OK, divided by 24 and it vibrates out of 2128 per second times per second. And what we're gonna do is multiply 24 both sides by 24. So 128 times 24 gives us 3072 which is equal to UK. You rewrite this equation as the is equal to 3072 divided by l and for us to find the length of the string at work that vibrates at 64 times for a second. So we multiply l by both sides, 64 0 is equal to 3072. And lastly, we're gonna um divide both sides by 64 which gives us out is equal to 48. So 48 is the length of this string 48 inches.

So when we have a string vibrating under a constant tension, it's going to vary inversely with the length of the strain. So the rate of the vibration we're gonna go ahead and call our and the string length Let's call l and we need to go ahead and set up a inverse, very skinny inverse variation equation with this. So the vibration are is varying inversely So K R constant over l is going to represent the relationship between these variables. We're told that the string is 24 inches long and vibrating 128 times per second. So with that, we could go ahead and find a specific equation. So I'm gonna say that the 128 which is my rate, equals my constant K that I need to find over the length 24 inches to solve them and multiply by 24. And I get that Kay equals 3072. So when I go ahead and set up my equation, I've got that are equals that 3072 the constant I found over the length of the stream and this equation is gonna model any inverse variation between the rate of the vibration and the length of the stream. So when in the next portion, they ask me what is the length of a string that vibrates 64 times per second? While now I've got that are equals 64 l is what I need to find. So I'm gonna go ahead and plug this right into the equation that I'm gonna say 64 equals 3072 divided by l. And then I'm gonna go ahead and set up a proportion to make this nice and easy. We'll do a little cross multiplication. So 64 el equals one times 3072 Divide by 64 to get along, and we know that l the length of the stream equals 48 inches.


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