Question 46: Waves

Question

A closed organ pipe $$150 \mathrm{~cm}$$ long gives 7 beats per second with an open organ pipe of length $$350 \mathrm{~cm}$$, both vibrating in fundamental mode. The velocity of sound is __________ $$\mathrm{m} / \mathrm{s}$$.

Accepted Answer

$$\begin{aligned}
& \mathrm{f}_{\mathrm{c}}=\frac{\mathrm{v}}{4 \ell_1} \quad \mathrm{f}_{\mathrm{o}}=\frac{\mathrm{v}}{2 \ell_2} \
& \left|\mathrm{f}_{\mathrm{c}}-\mathrm{f}_0ight|=7 \
& \frac{\mathrm{v}}{4 	imes 150}-\frac{\mathrm{v}}{2 	imes 350}=7 \
& \frac{\mathrm{v}}{600 \mathrm{~cm}}-\frac{\mathrm{v}}{700 \mathrm{~cm}}=7 \
& \frac{\mathrm{v}}{6 \mathrm{~m}}-\frac{\mathrm{v}}{7 \mathrm{~m}}=7 \
& \mathrm{v}\left(\frac{1}{42}ight)=7 \
& \mathrm{v}=42 	imes 7 \
& =294 \mathrm{~m} / \mathrm{s}
\end{aligned}$$

Waves

A closed organ pipe $150 \mathrm{~cm} long gives 7 beats per second with an open organ pipe of length 350 \mathrm{~cm}, both vibrating in fundamental mode. The velocity of sound is __________ \mathrm{m} / \mathrm{s}$.

Integer / Numeric Answer Type