Question 258: Waves

Question

The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by $25 \%$ by keeping tension same then frequency change of second harmonic is

Accepted Answer

From the law of length for a vibrating string
$$ \begin{array}{ll}  & \mathrm{n}_2 l_2=\mathrm{n}_1 l_1 \ 	herefore & \mathrm{n}_2=\frac{l_1}{l_2} 	imes \mathrm{n}_1=\frac{l_1}{1.25 l_1} \mathrm{n}_1=0.8 \mathrm{n}_1 \ 	herefore & \mathrm{n}_1-\mathrm{n}_2=\mathrm{n}_1(1-0.8)=0.2 \mathrm{n}_1 \ & \frac{\mathrm{n}_1-\mathrm{n}_2}{\mathrm{n}_1}=0.2=20 \% \end{array} $$
Frequency is inversely proportional to length. Therefore, the frequency decreases by $20 \%$.

Answer

increased by $20 \%$

Answer

decreased by $20 \%$

Answer

increased by $10 \%$

Answer

decreased by $10 \%$

Waves

The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by 25 \% by keeping tension same then frequency change of second harmonic is

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