JEE MAIN - Physics (2024 - 8th April Morning Shift - No. 21)
A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\frac{a-1}{a}\right)$$ then the value of $$a$$ is _________.
Odpověď
16
Vysvětlení
$$\begin{aligned}
& f_o=\frac{v}{2 I} \quad \Rightarrow \quad f_{o_7}=8 \frac{v}{2 l} \\
& f_c=\frac{v}{4 I} \quad \Rightarrow \quad f_{c_7}=15 \frac{v}{4 I} \\
& \frac{f_{c_7}}{f_{o_7}}=15 \frac{v}{4 I} \frac{2 l}{8 v}=\frac{30}{32}=\frac{15}{16}
\end{aligned}$$