Question 371: Waves

Question

A tuning fork gives 3 beats with $$50 \mathrm{~cm}$$ length of sonometer wire. If the length of the wire is shortened by $$1 \mathrm{~cm}$$, the number of beats is still the same. The frequency of the fork is

Accepted Answer

The frequency of a vibrating wire $$f=\frac{1}{2 l} \sqrt{\frac{T}{m}}$$
$$	herefore \quad \mathrm{f} \propto \frac{1}{l} \Rightarrow \mathrm{fl}=$$ constant
Let the frequency of the fork be $$f$$ and the initial and final frequencies of the wire be $$f_1$$ and $$f_2$$.
The number of beats heard before decreasing the length is $$f-f_1=3$$ .... (i)
The number of beats after decreasing the length is $$\mathrm{f}_2-\mathrm{f}=3$$ .... (ii)
$$	herefore \quad \mathrm{f}_1 l_1=\mathrm{f}_2 l_2$$
$$	herefore (\mathrm{f}-3) 50=(\mathrm{f}+3) 49 \quad$$ ... from (i) and (ii)
$$\quad 50 \mathrm{f}-49 \mathrm{f}=147+150$$
$$	herefore \quad \mathrm{f}=297 \mathrm{~Hz}$$

Answer

256 Hz

Answer

288 Hz

Answer

297 Hz

Answer

320 Hz

Waves

A tuning fork gives 3 beats with $50 \mathrm{~cm} length of sonometer wire. If the length of the wire is shortened by 1 \mathrm{~cm}$, the number of beats is still the same. The frequency of the fork is

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