At a temperature of 27^ C , two identical organ pipes produce notes of frequency 140 ~Hz . If the temperature of one pipe is raised to 57.75^ C , then the number of beats produced per second is

Step-by-step solution

Here, n₀=140 ~Hz , T₀=27^ C =300 ~K and T₂=57.75^ C =330.75 ~K The variation of speed of sound with temperature, v_t v₀ = T T₀ Let v₀= speed of sound at the room temperature. v_t=v₀ 330.75 300 =1.05 v₀ Hence, the beats produced in oragan pipe. Number of beats, n=n_t-n₀=140 1.05-140=7 ( n_t= v_t 4 L and n₀= v₀ 4 L ) So, the correct option is (a).