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 organ pipe is
  • A$\frac{L}{3}$
  • B$\frac{{4L}}{3}$
  • C$\frac{{4L}}{3}\sqrt {\frac{{{\rho _1}}}{{{\rho _2}}}} $
  • D$\frac{{4L}}{3}\sqrt {\frac{{{\rho _2}}}{{{\rho _1}}}} $
IIT 2004, Diffcult
art

Download our app
and 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

  • 1
    In a resonance tube, the first resonance is obtained when the level of water in the tube is at $16\,cm$ from the open end. Neglecting end correction, the next resonance will be obtained when the level of water from the open end is .... $cm$
    View Solution
  • 2
    The fundamental frequency of a sonometer wire is increases by $6\, Hz$ if its tension is increased by $44\%$, keeping the length constant. The frequency of the wire is ...... $Hz$
    View Solution
  • 3
    The linear density of a vibrating string is $1.3 \times 10^{-4}\, kg/m.$ A transverse wave is  propagating on the string and is described by the equation $Y = 0.021\, \sin (x + 30t)$ where $x$ and $y$ are measured in meter and $t$ in second the tension in the  string is ..... $N$
    View Solution
  • 4
    A transverse wave is represented by $y= Asin $ $\left( {\omega t - kx} \right)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?
    View Solution
  • 5
    The stationary wave $y = 2a\sin kx\cos \omega \,t$ in a closed organ pipe is the result of the superposition of $y = a\sin (\omega \,t - kx)$ and
    View Solution
  • 6
    First overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. Further nth harmonic of closed organ pipe is also equal to the mth harmonic of open pipe, where $n$ and $m$ are:
    View Solution
  • 7
    The given diagram shows a detector placed between a transmitter of sound waves and a metal plate. At three adjacent points, $ R, S$ and $T$ , the meter shows zero intensity. Which of the following is the frequency of the emitted wave ... $Hz$ ? (Take the velocity of sound as $ = 300\ m/s$ )
    View Solution
  • 8
    The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative $x$-axis. Identify the correct statement $(s)$ related to the movement of the points shown in the figure. The points moving in the direction of wave are
    View Solution
  • 9
    Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $n_1$ and the other with frequency $n_2$. The ratio $n_1/n_2$ is given by
    View Solution
  • 10
    The speed of sound in a gas, in which two waves of wavelength $1.0\,\, m$ and $1.02\,\, m$ produce $6$ beats per second, is approximately .... $m/s$
    View Solution