A student is performing the experiment of Resonance Column. The diameter of the column tube is 4cm . The distance frequency of the tuning for k is 512 Hz. The air temperature is 38 C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top and of the Resonance column. When first resonae occurs, the reading of the water level in the column is

Ajaykrishnan Jayagopal
11 Points
9 years ago
For an air column of length ’L’ closed at one end, the wavelength of the nth mode of vibration ’x’ is given by:     L=(4n+1)*(x/4)  , where n=0,1,2,3,...
For first resonance, n=0.
L=x/4
x=4L
Now,  x*f=v
where, f= frequency of vibrations = 512 Hz
v=velocity of sound=336 m/s
Therefore,
4L=v/f
L= v/(4*f)
L= 336/(4*512)  m = 0.164 m = 16.40 cm from the top.

askIITians Faculty 628 Points
3 years ago
Dear student,

For an air column of length ’L’ closed at one end, the wavelength of the nth mode of vibration ’x’ is given by:     L=(4n+1)*(x/4)  , where n=0,1,2,3,...
For first resonance, n=0.
L=x/4
x=4L
Now,  x*f=v
where, f= frequency of vibrations = 512 Hz
v=velocity of sound=336 m/s
Therefore,
4L=v/f
L= v/(4*f)
L= 336/(4*512)  m = 0.164 m = 16.40 cm from the top.

Thanks and regards,
Kushagra