A tuning fork of frequency 392 Hz, resonates with 50 cm length of a string under tension T. If the length of the string is decreased by 2% keeping the tension constant the number of beats heard when the string and the tuning fork are made to vibrate simultaneously is

Options

A. 8
B. 12
C. 4
D. 6

Answer

A

Explanation

Frequency of string `n=1/(2l)sqrt(T/m)`
`nprop1/l`
`n_1/n_2=l_2/l_1`
`n_1=392,l_1=l,l_2=l=l-(lxx2)/100=98/100l,n_2=?`
`392/n_2=(98/100l)/l`
`impliesn_2=(392xx100)/98=400"Hz"`
`:.` Number of beats = `n_2-n_1=400-392=8`