Question

When tension in a string is 225 N, then vibrating in fundamental mode it produces 6 beats per second with a tuning fork. The same string, when under tension of 256 N, again vibrating in fundamental mode produces with the same tuning fork 6 beats per second. Then, the frequency of the tuning fork is:

• A. 256 Hz
• B. 255 Hz
• C. 240 Hz
• D. 186 Hz

Answer 1

The correct option is D 186 Hz

$f_1=\frac{1}{2l}\sqrt{\frac{225}{m}}=\frac{15}{2l}\sqrt{\frac{1}{m}}$,

$f_2=\frac{1}{2l}\sqrt{\frac{256}{m}}=\frac{16}{2l}\sqrt{\frac{1}{m}}$,

$f_2-f_1=\mathrm{6.......}\left(1\right)$ and $f_1-f_2=6...................\left(2\right)$

adding equations (1) and (2), and substituting the values of $f_1$,

and $f_2$,

$\frac{1}{2l}\sqrt{\frac{1}{m}}=12$

$f_1=15\times 12=180Hz$

from(1), $f_2=186Hz$

Option "D" is correct.