Question

Suppose you pluck a string on a guitar and it produces the note A at a frequency of 440 Hz. Now you press your finger down on the string against one of the frets, making this point the new end of the string. The newly shortened string has 4/5 the length of the full string. When you pluck the string, its frequency will be
A. 350 Hz
B. 440 Hz
C. 490 Hz
D. 550 Hz

Answer 1

Answer:

D. 550 Hz

Explanation:

Frequency for string is given by

$f_{} =\frac{v}{2L}$

where v is the speed of the wave, L = m is the length

Frequency is inversely proportional to the Length of the string

$f \alpha \frac{1}{L}$

from above relation we can write

$\frac{f_{1}}{f_{2}} =\frac{L_{2}}{L_{1}}$

The newly shortened string has 4/5 the length of the full string .i,e

$\frac{440}{f_{2}} =\frac{\frac{4}{5}L_{1} }{L_{1}}\\f_{2}=\frac{440\times5}{4} \\f_{2}=550 Hz$

Hence option D is correct