Question

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is:
A. 66.7 cm
B. 100 cm
C. 150 cm
D. 200 cm

Answer 1

Hint: The smallest length at which the resonance occurs in the given air column is equal to one fourth of the wavelength of the sound waves. The next resonating length is at a distance which is equal to three times the length of the smallest length at which the resonance occurs.

Complete step-by-step answer:
We are given an air column which is closed at one end and open at the other. It resonates when a tuning fork is brought near the open end of the air column. We are given the smallest length of the column at which the resonance occurs. This distance is equal to one-fourth of the wavelengths of the sound waves produced by the tuning fork. It is given as
$\dfrac{\lambda }{4} = 50cm$
Here $\lambda $ is the wavelength of the sound waves that are generated by the tuning fork.
Now the next larger length of the column at which the resonance occurs with the tuning fork is three times greater than the smallest length at which the resonance occurs. It can be written as
$\dfrac{{3\lambda }}{4} = 3 \times 50 = 150cm$
So, the next larger length of the column resonating with the same tuning fork is 150 cm. Hence, the correct answer is option C.

So, the correct answer is “Option c”.

Note: It should be noted that in the given case of the air column, the resonance is a phenomenon in which at a certain frequency or wavelength, the particle of the medium in the air column vibrates at very high amplitude. The distance at which this resonance occurs in the air column is decided by the wavelength of the sound waves that are generated by the tuning fork.