Wave Motion 5 Question 15

15. A student is performing an experiment using a resonance column and a tuning fork of frequency 244s1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350±0.005)m, the gas in the tube is

(2014 Adv.) (Useful information : 167RT=640J1/2mole1/2; 140RT=590J1/2mole1/2. The molar masses M in grams are given in the options. Take the value of 10/M for each gas as given there.)

(a) Neon (M=20,10/20=7/10)

(b) Nitrogen (M=28,10/28=3/5)

(c) Oxygen (M=32,10/32=9/16)

(d) Argon (M=36,10/36=17/32)

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Solution:

  1. Minimum length =λ4

λ=4l

Now,

v=fλ=(244)×4×l

as

l=0.350±0.005

v lies between 336.7m/s to 346.5m/s

Now, v=γRTM×103, here M is molecular mass in gram

=100γRT×10M

For monoatomic gas, γ=1.67

v=640×10M

For diatomic gas, γ=1.4

v=590×10MvNe=640×710=448m/s vAr=640×1732=340m/svO2=590×916=331.8m/s

vN2=590×35=354m/s

Only possible answer is Argon.



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