Wave Motion 2 Question 5

5. A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512Hz produces first resonance when the tube is filled with water to a mark 11cm below a reference mark. near the open end of the tube. The experiment is repeated with another fork of frequency 256Hz which produces first resonance when water reaches a mark 27cm below the reference mark. The velocity of sound in air, obtained in the experiment is close to (Main 2019, 12 Jan II)

(a) 328ms1 (b)

(b) 341ms1

(c) 322ms1

(d) 335ms1

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Answer:

Correct Answer: 5. (a)

Solution:

  1. Key idea To overcome the error occured in measurement of resonant length. We introduce end correction factor e in length.

In first resonance, length of air coloumn =λ4.

So, l1+e=λ4 or 11×4+4e=λ

So, speed of sound is

v=f1λ=512(44+4e)

And in second case,

l1+e=λ4 or 27×4+4e=λv=f2λ=256(108+4e)

Dividing both Eqs. (i) and (ii), we get

1=512(44+4e)256(108+4e)e=5cm

Substituting value of e in Eq. (i), we get

Speed of sound v=512(44+4e)

=512(44+4×5)=512×64cms1=327.68ms1328ms1



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