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

• A. 200
• B. 210
• C. 205
• D. 215

Answer 1

Answer: (C)

205

Answer 2

Let the frequency of tuning fork be N

As the frequency of vibration string $\propto \frac{1}{\text{length}\mspace{6mu}\text{of} ⥂ \text{string}}$

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 tuning fork produces 5 beats/sec with sonometer wire

Hence $n_{1}l_{1} = n_{2}l_{2}$ ⇒ $(N + 5) \times 20 = (N - 5) \times 21$

⇒ $N = 205Hz.$