Question

A tuning fork vibrating with a sonometer wire of length $20cm$ produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to $21cm$. The frequency of the tuning fork must be:

• A. $200Hz$
• B. $210Hz$
• C. $205Hz$
• D. $215Hz$

Answer 1

Answer: (C)

$205Hz$

2 X beat $={\delta }_1^5-{\delta }_2^5$

$2\times 5=\frac{\vartheta }{2l_1}-\frac{\vartheta }{2l_2}$

$2\times 5=\frac{\vartheta }{2}(\frac{1}{20}-\frac{1}{21})$

$\vartheta =\frac{2\times 5\times 2\times 20\times 21}{21-20}$$=8400cm/s$

${\delta }_1^5=\frac{8400}{2\left(20\right)}=210Hz$

Now, $beat={\delta }_1^5-$ tuning fork frequency $\left({\delta }_T\right)$

$5=210-{\delta }_T$

=> Tuning fork frequency $\left({\delta }_T\right)=205Hz$