A source of sound S in the form of a block kept on a smooth horizontal surface is connected to a spring, as shown in the figure. If the spring oscillates with an amplitude of 50 ~cm along horizontal between the wall and the observer O , the maximum frequency heard by the observer is 12.5 % more than the minimum frequency heard by him. If the mass of the source of sound is 100 ~g , the force constant of the spring is

Step-by-step solution

Given, amplitude of spring, A=50 10⁻² ~m , maximum frequency heard by observer, n_ max =1.125 n_ min mass of sound source, m=100 ~g =0.10 ~kg and speed of sound, v=340 ~ms ⁻¹ . As, the apparent frequency heard by observer for moving source, n= n₀ v v-v_s Hence, for n_ , v_s=v_ s and for n_ , v_s=-v_ s By dividing Eqs. (i) by (ii), we get aligned & 1.125 n_ n_ = v+v_ s v-v_ s & 1.125 (v-v_ s )= (v+v_ s ) & v(0.125)=2.125 v_ s & 340 0.125 2.125 =v_ s & aligned From Eqs. (iii) and (iv), we get aligned k & = v_ s ^2 m