The frequency of vibration of a guitar string under constant tension varies inversely as the length of the string. A guitar string with a length of 20 inches has a frequency of 270 vibrations per second. Find the frequency of a guitar string with a length of 16 inches. Assume the tension is the same for both strings. Round answer to nearest whole vibration.
A)360 vibrations/s
B)277 vibrations/s
C)338 vibrations/s
D)216 vibrations/s
E)349 vibrations/s

Question

Quizplus · Accepted Answer

We can use the inverse variation formula:

frequency = k/length

where k is the constant of proportionality. We can find k by using the given information for the first string:

270 = k/20

k = 5400

Now we can use k to find the frequency of the second string:

frequency = 5400/16

frequency ≈ 337.5 ≈ 338 (rounded to nearest whole vibration)

Therefore, the frequency of the second string is approximately 338 vibrations per second, which is closest to choice C.

The Frequency of Vibration of a Guitar String Under Constant