Question

Two tuning forks, A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is

• A. 250 Hz
• B. 252 Hz
• C. 254 Hz
• D. 256 Hz

Answer 1

Answer: (C)

254 Hz

Answer 2

Here, $\upsilon_{A} = 258Hz,\upsilon_{B} = 262Hz$

Let the frequency of unknown tuning fork be $\upsilon.$ It produces $\upsilon_{b}$ beats with A and $2\upsilon_{b}$with B.

Therefore ,

$\upsilon_{A} - \upsilon = \upsilon_{b}$ …… (i)

And $\upsilon_{B} - \upsilon = 2\upsilon_{b}$ …… (ii)

Subtract (i) from (ii) , we get

$\upsilon_{B} - \upsilon_{A} = \upsilon_{b}$

Substituting the given values, we get

$262 - 258 = \upsilon_{b}$

$\upsilon_{b} = 4Hz$

From (i), $\upsilon = \upsilon_{A} - \upsilon_{b} = (258 - 4)Hz = 254Hz$