Two tuning forks A and B sounded together give 8 beats/s. With an air resonance tube closed at one end, the…
Two tuning forks A and B sounded together give 8 beats/s. With an air resonance tube closed at one end, the two forks give resonances when the two air columns are 32 cm and 33 cm, respectively. Calculate the frequencies of forks.
Solution
Sol. Let the frequency of the first fork be $f_1$ and that of second be $f_2$.
Then, $f_1=\dfrac{v}{4\times 32}$ and $f_2=\dfrac{v}{4\times 33}$
⇒ $f_1 > f_2$
∴ $f_1 - f_2 = 8$ ...(i)
and
$\dfrac{f_1}{f_2} = \dfrac{33}{32}$ ...(ii)
Solving Eqs. (i) and (ii), we get
$f_1 = 264\ \text{Hz}$
and
$f_2 = 256\ \text{Hz}$
Answer: $f_1 = 264\ \text{Hz}$ and $f_2 = 256\ \text{Hz}$