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
Step 1: Identify the type of resonance tube and its resonant frequencies. The problem describes a resonance tube closed at one end. For a tube closed at one end, the resonant frequencies are given by the formula: f_n = ((2n-1)v)/(4L) where v is the speed of sound, L is the length of the tube, and n = 1, 2, 3, represents the harmonic number (odd harmonics only). Step 2: Determine the lowest resonant frequency (f_1). The lowest frequency corresponds to n=1. This is the fundamental frequency or the first harmonic. f_1 = ((2(1)-1)v)/(4L) = (1v)/(4L) = (v)/(4L) Step 3: Determine the next resonant frequency (f_2). The next resonant frequency after the fundamental corresponds to n=2. This is the first overtone or the third harmonic. f_2 = ((2(2)-1)v)/(4L) = (3v)/(4L) Step 4: Calculate the ratio (f_2)/(f_1). Now, we find the ratio of the next resonant frequency to the lowest resonant frequency: (f_2)/(f_1) = (3v)/(4L)(v)/(4L) (f_2)/(f_1) = (3v)/(4L) × (4L)/(v) (f_2)/(f_1) = 3 The ratio (f_2)/(f_1) is 3. The final answer is B. 3.