Question

54. An open pipe 30 cm long and a closed pipe
23 cm long, both of the same diameter, are each
sounding their first overtone are in unison. The end
correction of these pipes is
1) 0.5 cm 2) 0.3 cm 3) 1 cm 4) 1.2 cm​

Answer 1

Answer:

3) 1cm

Explanation:

Length of the open pipe = 30cm

Length of the closed pipe = 23cm

Let the velocity of light = V

Let the frequency of the note = n

When the open pipe is sounding its first overtone, the length of the pipe plus the end of the correction = λ

λ = v/n = 30+2c -- (1)

Since there are two end corrections, thus when the closed pipe is overtone -

3λ/4 = v/n = 23+c -- (2)

From 1 and 2

23+c = 3/4 × ( 30+2c)

92+4c = 90+6c

c = 1cm

Thus, the end  correction of these pipes is 1cm.

Answer 2

Answer:

THE ANSWER IS 1 CM

Explanation:

Length of the open pipe = 30cm

Length of the closed pipe = 23cm

Let the velocity of light = V

Let the frequency of the note = n

When the open pipe is sounding its first overtone, the length of the pipe plus the end of the correction = λ

λ = v/n = 30+2c -- (1)

Since there are two end corrections, thus when the closed pipe is overtone -

3λ/4 = v/n = 23+c -- (2)

From 1 and 2

23+c = 3/4 × ( 30+2c)

92+4c = 90+6c

c = 1cm

Thus, the end  correction of these pipes is 1cm.