Question

A guitar-like stringed instrument has a string that is 16 cm long. it sounds the musical note a (440 hz) when played without fingering. by what distance should you shorten it to play the note c (523 hz)

Answer 1

When played without using fingers, it produces the sound of the pitch a (440 Hz). You should shorten it to play the note c at a distance of 2.6 cm (523 Hz).

What is the frequency of the sound?

A sound pressure wave's frequency, also known as pitch, is the number of times it repeats itself every second.

Speed of wave propagation is directly proportional to the square root of the tension of the string and inversely proportional to the square root of linear density

$\rm v = \sqrt{\frac{T}{u}}$

Speed of the wave is the product of the frequency and the wavelength. The fundamental frequency wavelength is two times the string length.

f= 2L

V= f × λ

440×2×0.16 = 523×2L

L = 0.134 m

L = 13.4 cm

The string length for playing note C  will be 13.4 cm

The distance up to which hand is to be put so that the C note will play;

L=16- 13.4

L= 2.6 cm

Hence,at a distance  of  2.6 cm you should shorten it to play the note c (523 hz).

To learn more about the frequency of the sound, refer to the link brainly.com/question/1435829.

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