word problem?

Question

The frequency of vibration(f) in an open pipe organ varies invesely as the length (L) of the pipe. If the air in a pipe 2 meters long vibrates 60 times per minute, find the frequency in a pipe 1. meters long.

Can some one please explain the problem in baby steps?
I know it is a proportion problem, but I don't know how to set it up and solve it

Answer 1

as frequecy varies inversely with length, it means f = 1/L,

so the pipe vibrates 120 times when the L is 1 meter

Answer 2

First you have to understand the meaning of "varies inversely". If the pipe becomes shorter the vibration frequency increases. You can write this relationship as f=k/L where f is the frequency, L is the length, and k is a constant. You will observe in this relationship that if you increase L, f will become smaller; if you decrease L, f becomes larger.Why? L is in the denominator and being so when its magnitude increases the quotient (f)decreases; when its magnitude decreases the quotient (f) increases. That's the meaning of the given condition that the frequency varies inversely as the length.

Now let's go back to the problem. Substitute the given values in our equation: f=k/L, i.e. 60=k/2 . Let's call this A. Now the second given condition; f=k/1. Let's call this B.

Divide B by A:

f/60=(k/1)/(k/2). the k's will cancel out, and we get:

f/60=(1/1)/(1/2)
f/60=1/(1/2)
f/60=2

Multiply both sides by 60:

f=2(60)
f=120 times per minute.

We made an easy problem difficult, right? Actually since f varies inversely as the length, if 2 meters produces 60 vibrations, then 1 meter will produce 2 times that many vibrations or 60*2 equals 120 vibrations. You reduce L by 1/2 , f is doubled. Let's say we double L what will be the effect on f? It will be reduced by half. That's the meaning of inverse proportion.

Answer 3

Here's the trick. When two things vary inversely, it means that whenever you multiply them together, you always get the same number.

In this case the freqency (f) and the length (L) vary inversely. So fL is always the same. In the first instance we know f = 60 and L = 2. So fL = 120.

In the second case, we know f = 1, and since f and L vary inversely we know fL = 120. Therefore L = fL / f = 120 / 1 = 120 times per minute.

Another way to solve is knowing that when two things vary inversely, cutting one in half means you double the other. Here, we cut the length in half from 2 to 1 meter. So we need to double the frequency from 60 times per minute to 120 times per minute.

Answer 4

As f varies inversely as L, we have f = k/L, where k is a constant. Putting L=2 and f=60, we get k = 120

Therefore f = 120/L

f when L=1 equals 120 times per minute