A 80 cm long steel 2 g guitar string is adjusted to a tensio

A 80 cm long steel 2 g guitar string is adjusted to a tension of 900 N to tune to 220 Hz.

a) The linear density of the string is _____ g/m.

b) If the string is not in tune at 220 Hz, and one hears a beat frequency 3 Hz using a tuning fork, the possible frequencies of the un-tuned string are_____ Hz and _____ Hz.

c) To play the the 5th harmonic of 220 Hz, the distance from the bridge that the string is fingered is _____ m.

d) The frequency of the sound wave (in air) when the tuned string is played at full length is _____ Hz.

e) The wavelength of the sound wave striking the ear at 24 deg C from the tuned frequency of 220 Hz is _____ m.

Solution

(A) linear density = mass / length

         = 2g / 0.80 m = 2.5 g/m

(B) beat frequency = frequency diff

        = |f - f0|

3 = |f - 220|

f = 217Hz Or 223 Hz

(C) it will be 1/5 times of length.

L\' = 80/5 = 16 cm

(D) f = 220 Hz

(E) It will be same as 220 Hz.