Question

Jennifer is using a tuning fork to tune her fifth guitar string, which should be at a frequency of 110Hz, or note A2 in music terms. When she rings the tuning fork and plucks her guitar string, she hears 4.00beats/s.

(a) What are the two possible frequencies of Jennifer's guitar string?

(b) When Jennifer loosens the string slightly, she hears 3.00beats/s. What is the frequency of the guitar string?

(c) Guitar strings have a fundamental harmonic with a wavelength of 1.22m. What is the difference in the wave speed of the string when properly tuned and what it is in part (b), Δv=v0−vb?

Answer 1

a) Beats frequency is the difference of two frequencies

Therefore

b) Frequency of guitar string is given by

On loosening string the tension will decrease hence frequency of guitar wil decrease.

Now beat frequency is 3.00 beats/s

two possible frequency now are

earlier possible frequencies were

Since frequency must decrease on loosening therefore now the correct frequency will be 113hz while correct frequency for part (a) will be 114 hz

Since frequency must decrease on loosening therefore now the correct frequency will be 113hz while correct frequency for part (a) will be 114 hz