Question

At 16°C, two open-end organ pipes, when sounded together produce 34 beats in 2 seconds. How many beats per second will be produced if the temperature rises to 51°C? Neglect the increase in the length of the pipes.

• A. (A) 18
• B. (B) 15
• C. (C) 10
• D. (D) 5

Answer 1

Answer: (A)

(A) 18

Answer 2

Explanation:
Given:Number of beats produced per second at 16°C=342=17We have to find the number of beats per second that will be produced if the temperature rises to 51°CLetL1,L2= lengths of the two organ pipesv1,v2= lowest (or fundamental) frequencies emitted by the pipes at 16°Cv1′,v2′ = lowest frequencies emitted by the pipes at 51°Cv16,v51= velocities of sound at 16°C and 51°C respectively.The expression for fundamental frequency for a tube open at both ends is given byv=v2Lv1=v162L1 and v2=v162L2Beat frequency at 16∘C=v1−v2=17 (given)⇒v162L1−v162L2=17⇒v16[12L1−12L2]=17....(i)Let the number of beats per second at 51∘C=bThen, v1−v2=b⇒v512L1−v512L2=b⇒v51[12L1−12L2]=b....(ii)Dividing eq. (ii) by eq. (i), we getv51v16=b1751+27316+273=b17[∵vt∝t+273]⇒b=17×324289=17×1817=18s−1Hence, the correct option is (A).