While determining the speed of sound in air using the resonance column, the air column resonates in the fundamental mode, with a tuning fork when its length is 0.1m . When this length is changed to 0.35m , the same tuning fork resonates with the first overtone. Find the end correction.

Question

While determining the speed of sound in air using the resonance column, the air column resonates in the fundamental mode, with a tuning fork when its length is 0.1m . When this length is changed to 0.35m , the same tuning fork resonates with the first overtone. Find the end correction. (A) 0.012m . (B) 0.025m . (C) 0.05m . (D) 0.024m .

Tardigrade Admin · Accepted Answer

Let Δ l be the end correction. Given that: The fundamental tone for a length 0.1m= first overtone for the length 0.35m . ∴ (v/4 (0.1 + Δ l))=(3 v/4 (0.35 + Δ l)) . Solving this equation we get, Îl=0.025m=2.5cm .

Q. While determining the speed of sound in air using the resonance column, the air column resonates in the fundamental mode, with a tuning fork when its length is $0.1 m$ . When this length is changed to $0.35 m$ , the same tuning fork resonates with the first overtone. Find the end correction.

$0.012 m$ .

$0.025 m$ .

$0.05 m$ .

$0.024 m$ .

Let $Δ l$ be the end correction. Given that:
The fundamental tone for a length $0.1 m =$ first overtone for the length $0.35 m$ .
$∴ \frac{v}{4 ( 0.1 + Δ l )} = \frac{3 v}{4 ( 0.35 + Δ l )}$ .
Solving this equation we get, $Δ l = 0.025 m = 2.5 c m$ .

Q. While determining the speed of sound in air using the resonance column, the air column resonates in the fundamental mode, with a tuning fork when its length is 0.1m . When this length is changed to 0.35m , the same tuning fork resonates with the first overtone. Find the end correction.

0.012m .

0.025m .

0.05m .

0.024m .