question_answer 57)

                  A tuning fork vibrating with a frequency of 512 Hz is kept close to the open end of a tub filled with water (Fig.). The water level in the tube is gradually lowered. When the water level is 17 cm below die open end, maximum intensity of sound is heard. If the room temperature is \[{{20}^{o}}C\], calculate                 (a) speed of sound in air at room temperature                 (b) speed of sound in air at \[{{0}^{o}}C\]                 (c) If die water in the tube is replaced with mercury, will there be any difference in your observations?

Answer:

                  (a) The air column in the tube between the mouth of the tube and level of water vibrate as in a closed end pipe. When intensity of sound is maximum, then the vibrating tuning fork is in resonance with the vibrating air in the column.                 In this case,                 \[\therefore \] \[\upsilon =\,v\,\times \,4L\,=512\,\,\times \,4\,\times \,17\,\times {{10}^{-2}}\]                 \[=348.16\,m{{s}^{-1}}\]                 (b) \[\frac{\upsilon }{{{\upsilon }_{{{20}^{o}}}}}\,=\,\sqrt{\frac{273}{273+20}}\,=\,\sqrt{\frac{273}{293}}\,=\,0.965\]                 \[\therefore \] \[{{\upsilon }_{0}}\,=0.96\,\,{{\upsilon }_{{{20}^{o}}}}\,=0.965\,\times \,348.\,16\,\,m{{s}^{-1}}\]                 \[=336\,m\,{{s}^{-1}}\]                 (c) Intensity of sound will be heard maximum i.e. resonance will take place when the water level is 17 cm below the open end of the tube. However, the intensity of sound may increase because more sound waves will be reflected by mercury than water.