Question

Suppose the B string on a guitar is 24" long and vibrates with a frequency of about 247 Hz. You place your finger on the 5th fret, which changes the length of the string to 18". Which note do you hear when you play the string?
a. D (about 294 Hz)
b. E (about 329 Hz)
c. G (about 392 Hz)

Answer 1

Answer:

b. E (about 329 Hz)

Explanation:

Given data:

Initial length of the string l1= 24 in

initial frequency f1= 247 Hz

changed length l2= 18 in

Then we have to find the changed frequency f2= ?

We already now that

frequency f ∝ 1/length of the string l

therefore,

$\frac{f_1}{f_2} =\frac{l_1}{l_2}$

⇒${f_2}=\frac{l_1}{l_2}\times{f_1}$

⇒${f_2}=\frac{24}{18}\times{247}$

⇒${f_2}=329.33 Hz$