Two identical flutes produce fundamental nodes of frequency $300\,Hz$ at $27\,^oC.$ If the temperature of air in one flute is increased to $31\,^oC,$ the numbe of the beats heard per second will be
Diffcult
Download our app for free and get started
Velocity of sound increases if the temperature increases. So with $\mathrm{v}=\mathrm{n} \lambda,$ if $\mathrm{v}$ increases $\mathrm{n}$ will increase
at $27^{\circ} \mathrm{C}, \mathrm{v}_{1}=\mathrm{n} \lambda,$ at $31^{\circ} \mathrm{C}, \mathrm{v}_{2}=(\mathrm{n}+\mathrm{x}) \lambda$
Now using $\mathrm{v} \propto \sqrt{\mathrm{T}} \quad(\because \mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}})$
$\frac{\mathrm{v}_{2}}{\mathrm{v}_{1}}=\sqrt{\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}}=\frac{\mathrm{n}+\mathrm{x}}{\mathrm{n}}$
$\Rightarrow \frac{300+\mathrm{x}}{300}=\sqrt{\frac{(273+31)}{(273+27)}}=\sqrt{\frac{304}{300}}=\sqrt{\frac{300+4}{300}}$
$\Rightarrow 1+\frac{\mathrm{x}}{300}=\left(1+\frac{4}{300}\right)^{1 / 2}=\left(1+\frac{1}{2} \times \frac{4}{300}\right)$
$\Rightarrow x=2$ $\left[\because(1+\mathrm{x})^{\mathrm{n}}=1+\mathrm{nx}\right]$
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
- 1A heavy ball of mass $M$ is suspended from the ceiling of car by a light string of mass $m (m << M)$. When the car is at rest, the speed of transverse waves in the string is $60\, ms^{-1}$. When the car has acceleration $a$ , the wave-speed increases to $60.5\, ms^{-1}$. The value of $a$ , in terms of gravitational acceleration $g$ is closest toView Solution
- 2The disturbance $y (x, t)$ of a wave propagating in the positive. $x-$ direction is given by $y = \frac{1}{{1 + {x^2}}}$ at time $t\,= 0$ and by $y = \frac{1}{{\left[ {1 + {{\left( {x - 1} \right)}^2}} \right]}}$ at $t\, = 2\, s$, where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in $m/s$ isView Solution
- 3A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle $60^o$ with ground level. But he finds the aeroplane right vertically above his position. If $\upsilon $ is the speed of sound, speed of the plane isView Solution
- 4The wavelength of a particle is $99 cm$ and that of other is $100 cm$ Speed of sound is $396 m/s$. The number of beats heard isView Solution
- 5$50$ tuning forks are arranged in increasing order of their frequencies such that each gives $4 \,beats/sec$ with its previous tuning fork. If the frequency of the last fork is octave of the first, then the frequency of the first tuning fork is ... $Hz$View Solution
- 6Velocity of sound in airView Solution
$I.$ Increases with temperature
$II.$ Decreases with temperature
$III.$ Increase with pressure
$IV.$ Is independent of pressure
$V.$ Is independent of temperature
Choose the correct answer.
- 7Velocity of sound in airView Solution
$I.$ Increases with temperature
$II.$ Decreases with temperature
$III.$ Increase with pressure
$IV.$ Is independent of pressure
$V.$ Is independent of temperature
Choose the correct answer.
- 8The 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
- 9A tuning fork of frequency $340\,Hz$ resonates in the fundamental mode with an air column of length $125\,cm$ in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ $cm$View Solution
(Velocity of sound in air is $340\,ms ^{-1}$ )
- 10Figure shows a snapshot for a travelling sine wave along a string. Four elemental portions $a, b, c$ and $d$ are indicated on the string. The elemental portion which has maximum potential energy is/areView Solution
