SOLUTION: The frequency or number (f) of vibration of a string under constant tension is inversely proportional to the length (l) of the string. If a string of 48 cm vibrates 192 cycles

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Question 414299: The frequency or number (f) of vibration of a string under constant tension is inversely proportional to the length (l) of the string. If a string of 48 cm
vibrates 192 cycles per second, find the the constant of proportionality and the number of vibrations per second a string of 32 cm will make.
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
direct and inverse proportion formulas are shown below:
y = k*x (direct proportion)
y = k/x (inverse proportion)

Since you are dealing with inverse proportion, then the second formula applies.

k is the constant of proportionality.

you are given that a string of 48 cm vibrates 192 cycles per second.

you can use this fact to find the constant of proportionality.

let y = number of cycles per second.
let x = length of the string.

y = k/x becomes 192 = k/48

multiply both sides of this equation by 48 to get:

k = 192 * 48 = 9216

that's your constant of proportionality.

you apply that constant of proportionality when x = 32 cm.

you get y = 9216 / 32 = 288

the string will vibrate 288 cycles per second when the length of the string is 32 cm.

you can see that the proportion is inverse because, as the string length increases, the number of vibrations per second decreases.

you can also see that the ratio of the short string to the long string is inversely proportional as shown in the following table. 

long string          short string        ratio of short string to long string

l = 48               l = 32              32/48 = 2/3

vbs = 192            vbs = 288           288/192 = 3/2

l = length
vbs = vibrations per second


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The frequency or number (f) of vibration of a string under constant tension is inversely proportional to the length (l) of the string. If a string of 48 cm
vibrates 192 cycles per second, find the the constant of proportionality and the number of vibrations per second a string of 32 cm will make.
----
f = k/L
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Find "k" using "a string of 48 cm
vibrates 192 cycles per second".
---
192 = k/48
k = 9216 (constant of proportionality)
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Equation:
Find "the number of vibrations per second a string of 32 cm will make"
using y = 9216/L
y = 9216/32 = 288 vibrations per second
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Cheers,
Stan H.
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