Two sound waves travel in the same medium along the same direction. The waves possess identical pressure amplitudes, but the first wave's wavelength is twice that of the second. If P₁ and P₂ denote the average power transmitted across a cross section by the first and second waves respectively, then

Step-by-step solution

The average power transmitted across a cross-section of area A by a sound wave is given by P = I A , where I is the intensity of the wave. The intensity of a sound wave in terms of its pressure amplitude P₀ is given by I = ( P₀)^2 2 v , where is the density of the medium and v is the speed of sound in the medium. Since both waves travel in the same medium, and v are the same for both waves. It is given that both waves have identical pressure amplitudes, so P₀ is also the same. Therefore, the intensity I is independ