Question

5) A 67 cm guitar string (density = 0.8 g/cm) is out of tune. The ambient temperature is 20 C. When tuning the guitar string against a 440 Hz tuning fork, the guitarist hears a beat frequency of 4 Hz. By tightening the string, it is tuned to A at 440 Hz.

a) What was the frequency of the untuned string?

b) How much did string tension change when tuning this string to 440 Hz?

Answer 1

(a)

The frequency of untunned string is either 436 Hz or 444 Hz.

As tightening the string, it is tuned to A at 440 Hz, the frequency increases.

So the frequency of untunned string is 436 Hz

(b)

The tension in the string is,

$T_2-T_1=4L^2f_2^2m/L-4L^2f_1^2m/L = 503 N$