While measuring the speed of sound by performing a resonance column experiment

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

Smart Achievers · Accepted Answer

(2)

$V = \sqrt{\frac{V R T}{M}} \Rightarrow V \propto \sqrt{T},$

$f = \frac{V}{4 l} \Rightarrow l \propto V,$

$l_{1} = 18 c m \Rightarrow l_{2} = 54 c m$

$l_{1}' > 18 c m \Rightarrow l_{2}' > 54 c m$

Solution

Q.
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

1 $18 > x$

2 $x > 54$

3 $54 > x > 36$

4 $36 > x > 18$

Ans.
(2)

$V = \sqrt{\frac{V R T}{M}} \Rightarrow V \propto \sqrt{T},$

$f = \frac{V}{4 l} \Rightarrow l \propto V,$

$l_{1} = 18 c m \Rightarrow l_{2} = 54 c m$

$l_{1}' > 18 c m \Rightarrow l_{2}' > 54 c m$

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Solution

Q. 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

1 18>x

2 x>54

3 54>x>36

4 36>x>18

Ans. (2) V=VRTM⇒V∝T, f=V4l⇒l∝V, l1=18cm⇒l2=54cm l1'>18cm⇒l2'>54cm