Question 351: Waves

Question

A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , it is again tuned with the same tuning fork, the number of beats remain unchanged. The frequency of tuning fork will be

Accepted Answer

Let n be frequency of tuning fork.
Let $\mathrm{n}_1, \mathrm{n}_2$ be frequency of wire at tension $\mathrm{T}_1, \mathrm{~T}_2$ respectively.
$$\begin{aligned}
\mathrm{n} & \propto \sqrt{\mathrm{~T}} \quad	ext{.... (i)}\
\mathrm{n}_1 & =\mathrm{n}-6 \quad	ext{.... (ii)}\
\mathrm{n}_2 & =\mathrm{n}+6\quad	ext{.... (iii)}
\end{aligned}$$
$$
\begin{array}{ll}
	herefore & \frac{\mathrm{n}_1}{\mathrm{n}_2}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{225}{256}}=\frac{15}{16} \
	herefore & \frac{\mathrm{n}-6}{\mathrm{n}+6}=\frac{15}{16} \quad	ext{... from (i), (ii), (iii)}\
	herefore & 16 \mathrm{n}-96=15 \mathrm{n}+90 \
	herefore & n=186 \mathrm{~Hz}
\end{array}$$

Answer

256 Hz

Answer

186 Hz

Answer

225 Hz

Answer

280 Hz

Waves

A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , it is again tuned with the same tuning fork, the number of beats remain unchanged. The frequency of tuning fork will be

Choose the correct answer: