Question

17.
In a resonance column tube first resonance is
obtained at a length of 17 cm and second
resonance at 53 cm. The length of third resonance
will be
(1) 85 cm
(2) 87 cm
13) 89 cm
(4) 90 cm​

Answer 1

Answer:

The length of the third resonance will be 90cm i.e.option (4).

Explanation:

This is the formula-based question.

The resonance length of the air column in the resonance tube is

$l=(2n+1)\frac{\lambda}{4}$            (1)

Where,

λ=wavelength of the wave

n=0,1,2,3....

Now the first resonance length of the air column in the resonance tube is

$l_1=(2\times 0+1)\frac{\lambda}{4}=\frac{\lambda}{4}$             (2)

The second  resonance length of the air column in the resonance tube is

$l_2=(2\times 1+1)\frac{\lambda}{4}=\frac{3\lambda}{4}$          (3)

By substracting (2) from (3) we get;

$l_2-l_1=l_2=\frac{3\lambda}{4}-\frac{\lambda}{4}=\frac{\lambda}{2}$      (4)

From the question, we have l₁= 17 cm and l₂=53 cm by placing them in equation (4) we get;

$\lambda=2(l_2-l_1)=2(53-17)=2\times 36=72cm$     (5)

Now,

The third resonance length of the air column in the resonance tube is;

$l_3=(2\times2+1)\frac{\lambda}{4}=\frac{5\lambda}{4}$            (6)

By placing the value of λ in equation (6) we get;

$l_3=\frac{5\times 72}{4}=90cm$

Hence, the length of the third resonance will be 90cm i.e.option (4).