Question

When tuning his guitar, a music student notices that the string is not vibrating at the desired frequency of 120 Hz, so he tightens the string by 15.5% to get this frequency. At what frequency was the string vibrating when he first started the tuning process

Answer 1

The original vibrating frequency of the guitar string before being tightened by 15.5% to reach 120 Hz was approximately 103.90 Hz.

Step-by-step explanation:

The music student tightened the guitar string by 15.5% to achieve the desired frequency of 120 Hz. To find the original frequency, we should calculate the frequency before the 15.5% increase. If the frequency after the tightening is 120 Hz (100% + 15.5% = 115.5% of the original frequency), then the original frequency (100%) can be found by dividing 120 Hz by 1.155.

The original vibrating frequency of the guitar string before being tightened by 15.5% to reach 120 Hz was approximately 103.90 Hz.

Original Frequency = 120 Hz / 1.155

Original Frequency ≈ 103.90 Hz

Therefore, the string was originally vibrating at approximately 103.90 Hz before the student tightened it.

Answer 2

Step-by-step explanation:

We know that

frequency ∝ √ Tension

So

Δn / n = 1/2 (ΔT / T)

Δn / n = .155 / 2 ( GIVEN )

= .0775

Δn = .0775 n

Let the original frequency be n

n +Δn = 120

n + .0775 n = 120

n = 111.36