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: Understand the resonance conditions for a closed-end tube. In a resonance tube (which is typically a closed-end tube due to the water column), resonance occurs when the length of the air column (L) is an odd multiple of a quarter wavelength. The formula for resonance lengths is: L_n = ((2n-1))/(4) where n = 1, 2, 3, represents the order of resonance. For the first resonance (n=1): L_1 = ((2(1)-1))/(4) = ()/(4) For the second resonance (n=2): L_2 = ((2(2)-1))/(4) = (3)/(4) For the third resonance (n=3): L_3 = ((2(3)-1))/(4) = (5)/(4) Step 2: Use the given first resonance position to find the wavelength (). The problem states that the first position of resonance is 16.50 \, cm from the open end. So, L_1 = 16.50 \, cm. Using the formula for the first resonance: L_1 = ()/(4) 16.50 \, cm = ()/(4) Now, solve for : = 4 × 16.50 \, cm = 66.00 \, cm Step 3: Calculate the distance to the next resonance position. The "next position where resonance occurs" refers to the second resonance (L_2). Using the formula for the second resonance: L_2 = (3)/(4) Substitute the calculated value of : L_2 = 3 × 66.00 \, cm4 L_2 = 3 × ((66.00)/(4)) \, cm L_2 = 3 × 16.50 \, cm L_2 = 49.50 \, cm The distance from the open end to the next position where resonance occurs is 49.50 cm.