Question

5) Resonance tube
A set of five tuning forks of known frequencies is given to you. Find correct length
of air column vibrating in unison with each tuning fork.
Hence determine the velocity of sound in air at room temperature,
88 ...​

Answer 1

Answer:

For finding the length of the tuning fork we can use the following relation

$f_1 : f_2 : f_3 : f_4 : f_5 = (2N_1 + 1) : (2N_2 + 1) : (2N_3 + 1) : (2N_4 + 1) : (2N_5 + 1)$

Also for velocity of sound in air we have

$v = 2(L_2 - L_1) f$

Explanation:

As we know that the tuning forks are in unison with the tube so we can say that

$f = \frac{(2N + 1)v}{4L}$

where N is an integer and its value will be different for all five tuning forks

so we can say that

$f_1 : f_2 : f_3 : f_4 : f_5 = (2N_1 + 1) : (2N_2 + 1) : (2N_3 + 1) : (2N_4 + 1) : (2N_5 + 1)$

now we can find the value of length of the tube by finding the values of N1, N2, N3, N4 and N5

Now we know that the velocity of sound in air is given as

$v = \lambda \times frequency$

so here for fundamental mode of frequency we have

$\frac{\lambda}{4} = L_1$

Now next resonance length is given as

$\frac{3\lambda}{4} = L_2$

so we have

$\frac{\lambda}{2} = (L_2 - L_1)$

now the velocity of sound is given as

$v = 2(L_2 - L_1) f$

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Topic : Resonance Tube experiment

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