While measuring the speed of sound by performing a resonance column experiment , a student gets the first resonance condition at a column length of 28cm during winter . Repeating the same experiment during summer , she measures the column length to be x cm for the second resonance. then , [AIEEE 2008]
Answers
Answer:
While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of
during winter. Repeating the same experiment during summer, she measures the column length to be
for the second resonance. Then
Explanation:
... ....
Explanation :- given L₁ = 18cm in winter season
Explanation :- given L₁ = 18cm in winter season column means pipe have one open and one closed ends so f = v₁/4L₁ (in column) [For 1st resonances]
same experiment during summer season . but in column , only odd harmonics
∴ f = 3v₂/ 4L₂ [for second resonance ]
where L₂ = x according to given situation and also v₁<v₂ as during summer temprature would be higher
⟹ 3v₂/4L₂ = v/4L₁ [∴frequency is same]
- L₂ = 3L₁ ×V₂/V₁
- L₂ = 3×18×v₂/v₁
- ⟹ x = 54×v₂/v₁
But as we know that speed of sound , 'v' = √γRT/M
v∝T so( in summer )absolutely v₂ will be greater that v₁
- ∴ X > 54 Answer