Question

A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats

per second. The beat frequency does not change if the length of the wire is

changed to 21 cm. the frequency of the tuning fork (in Hertz) must be

[UPSEAT 2000; Pb. PET 2004]

• A. 200
• B. 210
• C. 205
• D. 215

Answer 1

The correct option is C

205

Let the frequency of tunning fork be N

As the frequency of vibration string
$\infty$ $\frac{1}{lengthofstrins}$
For sonometer wire of length 20 cm, frequency

must be (N + 5) and that for the sonometer

wire of length 21cm, the frequency must be

(N - 5) as in each case the tunning fork produces 5 beats/sec

with sonometer wire

Hence $n_1{l}_1=n_2{l}_2\Rightarrow (N+5)\times 20=(N-5)\times 20$
$\Rightarrow$ N = 205 Hz.