A string in a musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of 1000 Hz is to be produced, then required length of string is

Options

A. 62.5 cm
B. 40 cm
C. 50 cm
D. 37.5 cm

Answer

B

Explanation

Initial length of string ` (l_(1))=50 cm =0.5 m`
Initial fundamental frequency `(n_(1))=800 Hz ` and final frequency `(n_(2))=1000 Hz `.
Frequency of vibration of the string `, n=(1)/(2l)sqrt((T)/(m)) prop (1)/(l)`
`:. (n_(1))/(n_(2))=l_(2)/(l_(1)) or l_(2)=(n_(1) xx l_(1))/( n_(2)) =(800 xx 50)/(1000) =40 cm` . ( where ` l_(2)`= final length of the string )