While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18\ cm$ during winter. Repeating the same experiment during summer, she measures the column length to be $x\ cm$ for the second resonance. Then
AIEEE 2008, Medium
Download our app for free and get started
For first resonant length $v=\frac{v}{4 \ell_{1}}=\frac{v}{4 \times 18}$ (in winter)
For second resonant length
$v^{\prime}=\frac{3 v^{\prime}}{4 \ell_{2}}=\frac{3 v^{\prime}}{4 x} \text { (insummer) } \quad \therefore \frac{v}{4 \times 18}=\frac{3 v^{\prime}}{4 \times x}$
$\therefore \quad x=3 \times 18 \times \frac{v^{\prime}}{v} \quad \therefore x=54 \times \frac{v^{\prime}}{v} \mathrm{cm}$
$\mathrm{v}^{\prime}>\mathrm{v}$ because velocity of light is greater in summer as compared to winter $(\mathrm{v} \propto \sqrt{\mathrm{T}})$
$\therefore x>54 \mathrm{cm}$
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
- 1A certain string will resonant to several frequencies, the lowest of which is $200 \,cps$. What are the next three higher frequencies to which it resonants?View Solution
- 2The amplitude of two waves are in ratio $5 : 2$. If all other conditions for the two waves are same, then what is the ratio of their energy densitiesView Solution
- 3The velocity of sound in a gas at pressure $P$ and density $d$ isView Solution
- 4A second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The point where the string has to be plucked and touched areView Solution
- 5A wave represented by the equation $y_1 = a\,cos(Kx-\omega t)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation for the other wave isView Solution
- 6View SolutionCoherent sources are characterized by the same
- 7When two sound sources of the same amplitude but of slightly different frequencies $v_1$ and $v_2$ are sounded simultaneously, the sound one hears has a frequency equal toView Solution
- 8A siren emitting a sound of frequency $800\,\, Hz$ moves away from an observer towards a cliff at a speed of $15 \,\,m s^{-1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is .... $Hz$View Solution
(Take velocity of sound in air $= 330\,\, m s^{-1}$) - 9View SolutionAs a wave propagates
- 10Two wires are fixed in a sonometer. Their tensions are in the ratio $8 : 1$. The lengths are in the ratio $36:35.$ The diameters are in the ratio $4 : 1$. Densities of the materials are in the ratio $1 : 2$. If the lower frequency in the setting is $360 Hz.$ the beat frequency when the two wires are sounded together isView Solution