Question

A streched string is divided into two parts with the help of a wedge. The total length of the string is 1m and the two parts differ by2 mm. When sounded together they produced two beats per second. The frequencies of the notes emmitted by the two parts are then

• A. 400,500
• B. 251,249
• C. 600,700
• D. 800,0

Answer 1

The correct option is B 251,249

Given,

Difference in length is $2mm$

Length of $1^{st}$ string is $502mm$

Length of $2^{nd}$ string is $498mm$

$Frequency\alpha \frac{1}{Length}$

$\frac{f_1}{f_2}=\frac{L_2}{L_1}=\frac{504}{498}......\left(1\right)$

Beat frequency is $2$beat per second.

$|f_1-f_2|=2Hz......\left(2\right)$

Form equation (1) and (2)

$f_1=251Hzand{f}_2=249Hz$

Hence, frequency are $251Hzand249Hz$