Question 213: Waves

Question

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

Accepted Answer

For first resonant length $$v = {v \over {4{\ell _1}}} = {v \over {4 	imes 18}}$$ (in winter)
For second resonant length
$$v' = {{3v'} \over {4{\ell _2}}} = {{3v'} \over {4x}}$$ (in summer)
$$	herefore$$ $${v \over {4 	imes 18}} = {{3v'} \over {4 	imes x}}$$
$$	herefore$$ $$x = 3 	imes 18 	imes {{v'} \over v}$$
$$	herefore$$ $$x = 54 	imes {{v'} \over v}cm$$
$$v' > v$$ because velocity of light is greater in summer as compared to winter
$$\left( {v \propto \sqrt T } ight)$$
$$	herefore$$ $$x > 54\,cm$$

Answer

$$18 > x$$

Answer

$$x > 54$$

Answer

$$54 > x > 36$$

Answer

$$36 > x > 18$$

Waves

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

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