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.
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Here are the solutions to the problems: 17.1 The speed of a transverse wave on a stretched string is given by the formula v = sqrt((T)/()), where T is the tension in the string and is the linear mass density (mass per unit length) of the string. Both tension and linear density are properties of the medium that influence the speed of the wave. Wavelength and frequency are related to the speed (v = f) but do not determine the speed itself; rather, they are determined by the speed and each other. Therefore, both Tension (A) and Linear density of the string (D) are factors that influence the speed of the wave. Since this is a multiple-choice question and typically only one answer is expected, we will select the first correct option listed. The correct option is A. A. Tension 17.2 The sound intensity level in decibels is related to the sound intensity I by the formula: = 10 _10((I)/(I_0)) where I_0 is the reference intensity, which is the threshold of human hearing, I_0 = 1.0 × 10^-12\,W/m^2. Step 1: Set the given intensity level to 0 dB. 0\,dB = 10 _10((I)/(I_0)) Step 2: Divide by 10. 0 = _10((I)/(I_0)) Step 3: Convert the logarithmic equation to an exponential equation. 10^0 = (I)/(I_0) 1 = (I)/(I_0) Step 4: Solve for I. I = I_0 Step 5: Substitute the value of I_0. I = 1.0 × 10^-12\,W/m^2 The correct option is C. C. 1.0 × 10^-12\,W/m^2 17.3 The speed of sound in an ideal gas is given by the formula: v = sqrt(( RT)/(M)) where is the adiabatic index, R is the ideal gas constant, T is the absolute temperature, and M is the molar mass of the gas. From this formula, we can see that the speed of sound v is directly proportional to the square root of the absolute temperature T: v sqrt(T) Step 1: Let the initial velocity be v_1 at an absolute temperature T_1. v_1 = ksqrt(T_1) where k = sqrt(( R)/(M)) is a constant. Step 2: If the absolute temperature is doubled, the new temperature T_2 = 2T_1. Step 3: Calculate the new velocity v_2. v_2 = ksqrt(T_2) = ksqrt(2T_1) = sqrt(2) ksqrt(T_1) Step 4: Substitute v_1 = ksqrt(T_1) into the equation for v_2. v_2 = sqrt(2) v_1 Step 5: Approximate the value of sqrt(2). sqrt(2) ≈ 1.414 So, v_2 ≈ 1.414 v_1. The velocity of sound increases to approximately 1.4 times its original value. The correct option is A. A. It increases to 1.4 times its original value 17.4 This problem involves the Doppler effect for sound. When an observer approaches a stationary source, the observed frequency f' is given by the formula: f' = f ((v + v_o)/(v)) where f is the source frequency, v is the speed of sound in the medium, and v_o is the speed of the observer. Step 1: Identify the given values. Source frequency f = 444\,Hz. Observer speed v_o = (1)/(2)v (one-half the speed of sound). Step 2: Substitute the values into the Doppler effect formula. f' = 444\,Hz ((v + 1)/(2)vv) Step 3: Simplify the expression inside the parentheses. f' = 444\,Hz ((2v)/(2) + (v)/(2)v) f' = 444\,Hz ((3v)/(2)v) f' = 444\,Hz ((3)/(2)) Step 4: Calculate the observed frequency. f' = 444\,Hz × 1.5 f' = 666\,Hz The correct option is A. A. 666\,Hz 17.5 For a standing sound wave in a tube: At a closed end*, the air molecules cannot move, so there is no displacement. This point is a displacement node. At an open end*, the air molecules are free to move with maximum amplitude. This point is a displacement antinode. Therefore, a standing sound wave in a tube opened at one end has a displacement node at the closed end and a displacement antinode at the open end. The correct option is B. B. node, antinode