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
Alright — let's do this. 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 approximated to be proportional to the square root of the absolute temperature. Step 1: Convert the given temperatures from Celsius to Kelvin. The absolute temperature T_K is calculated by adding 273.15 to the Celsius temperature T_C. Initial temperature: T_0 = 0^ C = 0 + 273.15 = 273.15 K Final temperature: T = 25^ C = 25 + 273.15 = 298.15 K Step 2: Use the formula relating the speed of sound to absolute temperature. The speed of sound v is proportional to the square root of the absolute temperature T: v sqrt(T) Therefore, we can write the ratio of speeds at two different temperatures as: (v_T)/(v_0) = sqrt((T)/(T_0)) Where v_0 is the speed at T_0, and v_T is the speed at T. Step 3: Substitute the given values and calculate the speed of sound at 25^ C. Given v_0 = 1000 ms^-1 at T_0 = 273.15 K. We need to find v_T at T = 298.15 K. v_T = v_0 sqrt((T)/(T_0)) v_T = 1000 ms^-1 sqrt(298.15 K)273.15 K v_T = 1000 ms^-1 sqrt(1.091521) v_T = 1000 ms^-1 × 1.044759 v_T = 1044.759 ms^-1 Step 4: Round the result to the nearest whole number, as per the options provided. 1044.759 ms^-1 rounds to 1045 ms^-1. Comparing this to the given options: (A) 1043 ms^-1 (B) 1044 ms^-1 (C) 1045 ms^-1 (D) 1042 ms^-1 The calculated value matches option (C). The final answer is C) 1045 ms^-1. Send me the next one 📸