Question

The number of vibrations per second, v, of a guitar string varies directly as the square root of the tension, t, and inversely as the length of the string, l. If the number of vibrations per second is 6 when the tension is 225 kg and the length of the string is 0.6 m, determine the number of vibrations per second when the tension is 180 kg and the length of the string is 0.8 m.

Answer 1

Answer: the number of vibrations per second when the tension is 180 kg and the length of the string is 0.8 m is 3.6.

Explanation:

Let's start by writing the general equation that relates v, t, and l:

v ∝ √t / l

Here, the symbol ∝ means "is proportional to." We can also write this equation using a constant of proportionality k:

v = k * √t / l

Now, we can use the information provided in the problem to solve for the value of k:

6 = k * √225 / 0.6

Simplifying, we get:

k = 6 * 0.6 / √225

k = 0.48

Now that we have the value of k, we can use the equation to find the number of vibrations per second when the tension is 180 kg and the length of the string is 0.8 m:

v = 0.48 * √180 / 0.8

Simplifying, we get:

v = 3.6

Therefore, the number of vibrations per second when the tension is 180 kg and the length of the string is 0.8 m is 3.6.