A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = young’s modulus, $\rho$ = density, $\alpha$ = coefficient of linear expansion) then the frequency of transverse vibration is proportional to :
Advanced
Download our app for free and get started
Tension in the string is developed in the wire due to cooling. The compression due to cooling is balanced by the expansion due to tension generated. Thus
$\frac{F L}{A Y}=L \alpha \Delta T$
$\Longrightarrow$ tension $F=Y A \alpha \Delta T$
Frequency of vibration is given as $f=\frac{1}{2 L} \sqrt{\frac{F}{\mu}}$
$\Longrightarrow f \propto \sqrt{\frac{Y A \alpha \Delta T}{\mu}}$
since $\rho A L=\mu L$
$f \propto \sqrt{\frac{Y \alpha}{\rho}}$
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
- 1Consider the three wavesView Solution
${z_1},{z_2}$ and ${z_3}$ as${z_1} = A\sin (kx - \omega \,t)$, ${z_2} = A\sin (kx + \omega \,t)$ and ${z_3} = A\sin (ky - \omega \,t)$.
Which of the following represents a standing wave
- 2The displacement y of a particle in a medium can be expressed as: $y = {10^{ - 6}}\sin (100t + 20x + \pi /4)m,$ where $t$ is in second and $x$ in meter. The speed of wave is ... $m/s$View Solution
- 3The wave described by $y=0.25 \,sin\left[ {10\pi x - 2\pi t} \right]$, where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along theView Solution
- 4View SolutionIf you set up the ninth harmonic on a string fixed at both ends, its frequency compared to the seventh harmonic
- 5A car is moving towards a high cliff. The car driver sounds a horn of frequency $f$. The reflected sound heard by the driver has a frequency $2f$. If $v$ be the velocity of sound then the velocity of the car, in the same velocity units, will beView Solution
- 6A parallel beam of light is incident on a tank filled with water up to a height of $61.5 \,mm$ as shown in the figure below. Ultrasonic waves of frequency $0.5 \,MHz$ are sent along the length of the water column using a transducer placed at the top and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen? (Take, the speed of sound in water to be $1500 \,m / s$ )View Solution
- 7The driver of a car travelling with speed $30 \,\,m/s$ towards a hill sounds a horn of frequency $600\,\, Hz.$ If the velocity of sound in air is $330 \,\,m/s$, the frequency of reflected sound as heard by driver is .... $Hz$View Solution
- 8View SolutionA closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of lengths
- 9Two cars ${X}$ and ${Y}$ are approaching each other with velocities $36\; {km} / {h}$ and $72\; {km} / {h}$ respectively. The frequency of a whistle sound as emitted by a passenger in car ${X}$, heard by the passenger in car ${Y}$ is $1320 \;{Hz}$. If the velocity of sound in air is $340\; {m} / {s}$, the actual frequency of the whistle sound produced is ........ $Hz.$View Solution
- 10A pipe closed at one end produces a fundamental note of $412\,Hz.$ It is cut into two pieces of equal length the fundamental notes produced by the two pieces areView Solution