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

The newly frequency is 550 Hz.

(D) is correct option.

Step-by-step explanation:

Given that,

Frequency = 440 Hz

Newly length
`L'=(4)/(5)L`

If the length of the string is L

We need to calculate the frequency

Using formula of frequency

`f=(v)/(2L)`....(I)

We need to calculate the newly frequency

Using formula of frequency

`f'=(v)/(2L')`....(II)

Divided equation (II) and (I)

`(f')/(f)=(L)/(L')`

Put the value into the formula

`(f')/(440)=(L)/((4)/(5)L)`

`f'=440*(5)/(4)`

`f'=550\ Hz`

Hence, The newly frequency is 550 Hz.