This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Right hafsatjibril2006, let's go. Step 1: Convert temperatures to Kelvin. The speed of sound in a medium is generally dependent on its temperature. For many materials, especially in introductory physics, the speed of sound is often approximated to be proportional to the square root of the absolute temperature (in Kelvin). Given temperatures: Initial temperature T_1 = 0^ C Final temperature T_2 = 25^ C Convert these to Kelvin: T_1 = 0 + 273.15 = 273.15 K T_2 = 25 + 273.15 = 298.15 K Step 2: State the relationship between speed of sound and temperature. The speed of sound (v) in a medium is often approximated to be proportional to the square root of its absolute temperature (T): v sqrt(T) This means we can write the ratio of speeds at two different temperatures as: (v_2)/(v_1) = sqrt((T_2)/(T_1)) Step 3: Substitute the given values into the formula. Given: Initial speed v_1 = 1000 m s^-1 at T_1 = 273.15 K We need to find v_2 at T_2 = 298.15 K. v_2 = v_1 sqrt((T_2)/(T_1)) v_2 = 1000 m s^-1 × sqrt(298.15 K)273.15 K Step 4: Calculate the final speed. v_2 = 1000 m s^-1 × sqrt(1.091506) v_2 = 1000 m s^-1 × 1.04475 v_2 = 1044.75 m s^-1 Rounding to a reasonable number of significant figures (e.g., 3 or 4, consistent with the given 1000 m s^-1): v_2 ≈ 1045 m s^-1 The speed of sound at 25^ C is approximately 1045 m s^-1. Got more? Send 'em.