Question

52. (ii) a guitar string is 91 cm long and has a mass of 3.2 g. the vibrating portion of the string from the bridge to the support post is and the string is under a tension of 520 n. what are the frequencies of the fundamental and first two overtones?

Answer 1

The frequencies of the fundamental, first overtone, and second overtone are 221.49 Hz, 664.47 Hz, and 1107.45 Hz .

The frequency of a vibrating string is determined by its length, mass, and tension. The fundamental frequency is the lowest frequency that the string can vibrate at. The first overtone is the next highest frequency, and the second overtone is the next highest frequency after that.

Given the following parameters:

Length of the string (L) = 0.91 m

Mass of the string (m) = 0.0032 kg

Tension in the string (T) = 520 N

We can calculate the frequencies of the fundamental and first two overtones using the following formulas:

Fundamental frequency (f0) = v / (2L)

First overtone frequency (f1) = 3f0

Second overtone frequency (f2) = 5f0

where v is the speed of the wave on the string, which can be calculated using the following formula:

v = √(T/m)

Plugging in the values for L, m, and T, we get the following results:

Frequency Value (Hz)

f0 221.49

f1 664.47

f2 1107.45