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The persistence of sound in a room after the source of sound is turned off is called reverberation. The measure of reverberation time is the time required for sound intensity to decrease by $60 \,dB$. It is given that the intensity of sound falls off as $I_0 \exp \left(-c_1 \alpha\right)$ where $I_0$ is the initial intensity, $c_1$ is a dimensionless constant with value $1 / 4$. Here, $\alpha$ is a positive constant which depends on the speed of sound, volume of the room, reverberation time, and the effective absorbing area $A_e$. The value of $A_e$ is the product of absorbing coefficient (with value between $0$ and $1,1$ being a perfect absorber) and the area of the room. For a concert hall of volume $600 \,m ^3$, the value of $A_e$ (in $m ^2$ ) required to give a reverberation time of $1 s$ is closest to (speed of sound in air $=340 \,m / s$ )
A 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 alternatives
For a certain organ pipe, three successive resonance frequencies are observed at $425,595,$ and $765 \,Hz$ respectively, Taking the speed of sound in air to be $340 \,m / s$ the fundamental frequency of the pipe (in $Hz$ ) is .........
Two closed pipe produce $10$ beats per second when emitting their fundamental nodes. If their length are in ratio of $25 : 26$. Then their fundamental frequency in $Hz$, are
Equation of a progressive wave is given by $y = 4\sin \left\{ {\pi \left( {\frac{t}{5} - \frac{x}{9}} \right) + \frac{\pi }{6}} \right\}$. Then which of the following is correct
Two vibrating tuning forks produce progressive waves given by ${Y_1} = 4\sin 500\pi t$ and ${Y_2} = 2\sin 506\pi t.$ Number of beats produced per minute is
A narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at the positions right angle to each other. A source placed at $S$ generated a wave of intensity $I_0$ which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point $D$ where a detector is placed The maximum value of $\lambda$ to produce a maxima at $D$ is given by
A wave disturbance in a medium is described by $y(x,\,t) = 0.02\cos \,\left( {50\,\pi t + \frac{\pi }{2}} \right)\cos (10\pi x)$, where $ x$ and $y$ are in metres and $t$ in seconds