In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of $20.0 \,cm$ for a tuning fork of frequency $400 \,Hz$ is used. The velocity of the sound at room temperature is $336 \,ms ^{-1}$. The third resonance is observed when the air column has a length of ......... $cm$
JEE MAIN 2022, Diffcult
Download our app for free and get started
For first resonance
$\ell_{1}+ e =\frac{\lambda}{4}$
$\lambda=\frac{336}{400} \times 100 \,cm =84 \,cm \Rightarrow \frac{\lambda}{4}=21 \,cm$
$e =21-20=1 \,cm$
For third resonance
$\ell_{3}+ e =\frac{5 \lambda}{4}=105 \,cm \Rightarrow \ell_{3}=104 \,cm$
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
- 1Select the correct statement about the reflection and refraction of a wave at the interface between the medium $1$ and $2$ theView Solution
- 2The displacement $y$ (in $cm$) produced by a simple harmonic wave is $y = \frac{{10}}{\pi }\sin \left( {2000\pi t - \frac{{\pi x}}{{17}}} \right)$. The periodic time and maximum velocity of the particles in the medium will respectively beView Solution
- 3A string is stretched between fixed points separated by $75.0\, cm$. It is observed to have resonant frequencies of $420\, Hz$ and $315\, Hz$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is .... $Hz$View Solution
- 4View SolutionA closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio
- 5In a resonance tube experiment when the tube is filled with water up to height of $17.0\, cm$ from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5\, cm$. If the velocity of sound in air is $330\, m / s ,$ the tuning fork frequency is$......Hz$View Solution
- 6View SolutionStanding stationary waves can be obtained in an air column even if the interfering waves are
- 7View SolutionA device used for investigating the vibration of a fixed string or wire is
- 8A string is stretched between fixed points separated by $75.0\ cm$. It is observed to have resonant frequencies of $420\ Hz$ and $315\ Hz.$ There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is .... $Hz$View Solution
- 9A string in musical instrument is $50 cm$ long and its fundamental frequency is $800 Hz.$ If a frequency of $1000 Hz$ is to be produced, then required length of string is ..... $cm$View Solution
- 10Two wires are in unison. If the tension in one of the wires is increased by $2\%, 5$ beats are produced per second. The initial frequency of each wire is .... $Hz$View Solution