A closed organ pipe of length $L$ and an open organ pipe contain gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{ x }{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$ where $x$ is ......... . (Round off to the Nearest Integer)
JEE MAIN 2021, Diffcult
Download our app for free and get started
$f_{c}=f_{0}$
$\frac{3 V_{C}}{4 L}=\frac{2 V_{0}}{2 L^{\prime}}$
$\frac{3 V_{C}}{4 L}=\frac{V_{0}}{L^{\prime}}$
$L ^{\prime}=\frac{4 L }{3} \frac{ V _{0}}{ V _{ C }}=\frac{4 L }{3} \sqrt{\frac{ B \cdot \rho_{1}}{\rho_{2} \cdot B }}( B$ is bulk modulus)
$=\frac{4 L }{3} \sqrt{\frac{\rho_{1}}{\rho_{2}}}$
$x =4$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The equation of a travelling wave is given by$y = 0.5\sin (20x - 400t)$ where $x$ and $y$ are in meter and $t$ is in second. The velocity of the wave is .... $m/s$View Solution
- 2A transverse pulse generated at the bottom of a uniform rope of length $L$, travels in upward direction. The time taken by it to travel the full length of rope will beView Solution
- 3A travelling wave is partly reflected and partly transmitted from a rigid boundary. Let $a_i, a_r$ and $a_t$ be the amplitude of incident wave, reflected wave and transmitted wave and $I_i, I_r$ and $I_t$ be the corresponding intensities. Then choose the correct alternativesView Solution
- 4The two interfering waves have intensities in the ratio $9 : 4$. The ratio of intensities of maxima and minima in the interference pattern will beView Solution
- 5A hearing test is conducted on an aged person. It is found that her thresold of hearing is $20 \,dB$ at $1 \,kHz$ and it rises linearly with frequency to $60 \,dB$ at $9 \,kHz$. The minimum intensity of sound that the person can hear at $5 \,kHz$ isView Solution
- 6A wave is represented by the equation : $y = a\sin (0.01x - 2t)$ where $a$ and $x$ are in $cm$. velocity of propagation of wave is .... $cm/s$View Solution
- 7In an experiment to study standing waves, you use a string whose mass per length is $μ$ = $(1.0 ± 0.1) × 10^{-4}\ kg/m$ . You look at the fundamental mode, whose frequency $f$ is related to the length $L$ and tension $T$ of the string by the following equation $L$ = $\frac{1}{{2f}}\sqrt {\frac{T}{\mu }} $ You make a plot with $L$ on the $y-$ axis and $\sqrt T$ on the $x-$ axis, and find that the best fitting line is $y$ = $(8.0 ± 0.3) × 10^{-3}x + (0.2 ± 0.04)$ in $SI\ units$ . What is the value of the frequency of the wave (including the error)? Express your result in $SI\ unit\ (Hz)$View Solution
- 8An observer receives waves directly from a source of sound distant $120\,m$ in a big hall. He also receives waves reflected from the mid-point of $25\,m$ high ceiling. The wavelength of sound for constructive interference to take place between two waves, must be :View Solution
- 9$Assertion :$ The change in air pressure affects the speed of sound.View Solution
$Reason :$ The speed of sound in gases is proportional to the square of pressure. - 10Two open organ pipes of length $60 \mathrm{~cm}$ and $90 \mathrm{~cm}$ resonate at $6^{\text {th }}$ and $5^{\text {th }}$ harmonics respectively. The difference of frequencies for the given modes is . . . . . $\mathrm{Hz}$.View Solution
(Velocity of sound in air $=333 \mathrm{~m} / \mathrm{s}$ )