Question 456: Waves

Question

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $$150 \mathrm{~Hz}$$, then second overtone of open pipe. The fundamental frequency of open end pipe will be

Accepted Answer

The frequency of third overtone of closed pipe is
$$f_3=(2(3)+1) f_1=7 f_1$$
where, $$f_1=$$ fundamental frequency of closed pipe $$=\frac{v}{41}$$
The frequency of second overtone of open pipe is
$$f_2^{\prime}=(2+1) f_1^{\prime}=3 f_1^{\prime}$$
where, $$f_1^{\prime}=$$ fundamental frequency of open pipe $$=\frac{v}{2}=2 f_1$$
$$\begin{array}{lrl}
	ext { Given, } \quad f_3-f_2^{\prime}=150 \Rightarrow 7 f_1-3 f_1^{\prime}=150 \
\Rightarrow \quad 7 f_1-3\left(2 f_1ight)=150 \Rightarrow f_1=150 \mathrm{~Hz} \
	herefore \quad f_1^{\prime}=2 f_1=300 \mathrm{~Hz}
\end{array}$$

Answer

400 Hz

Answer

200 Hz

Answer

500 Hz

Answer

300 Hz

Waves

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $150 \mathrm{~Hz}$, then second overtone of open pipe. The fundamental frequency of open end pipe will be

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