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JEE Advanced 2018 Paper 2
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© examsnet.com
Question : 6
Total: 54
In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7cm and 83.9 cm. Which of the following statements is (are) true?
The speed of sound determined from this experiment is 332m/s
The end correction in this experiment is
0.9
cm
The wavelength of the sound wave is
66.4
cm
The resonance at
50.7
cm corresponds to the fundamental harmonic
Validate
Solution:
let
n
1
harmonic is corresponding to 50.7 cm &
n
2
harmonic is corresponding
83.9
cm
∴
λ
2
=
(
83.9
−
50.7
)
c
m
λ
2
=
33.2
c
m
λ
=
66.4
c
m
∴
λ
4
=
16.6
c
m
Length corresponding to fundamental mode must be close to
λ
4
&
50.7
cm must be an odd multiple of this length
16.6
×
3
=
49.8
cm.therefore
50.7
is 3rd harmonic
If end correction is e, then
e
+
50.7
=
3
λ
4
c
m
Speed of sound,
v
=
f
λ
∴
v
=
500
×
66.4
cm/sec
=
332.000
m/s
© examsnet.com
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