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: State the Doppler effect (6.1). The Doppler effect is the apparent change in the frequency (or pitch) of a sound wave detected by a listener, due to the relative motion between the source of the sound and the listener. Step 2: Determine the direction of motion for the 3148 Hz frequency (6.2). According to the Doppler effect, when a sound source moves towards a listener, the observed frequency is higher than the source frequency. From the graph, 3148 Hz is the higher observed frequency. Therefore, the detector records 3148 Hz when the train moves TOWARDS the detector. Step 3: Calculate the speed of the train (6.3). Let f_s be the frequency of the siren emitted by the train, v be the speed of sound in air (340 m/s), and v_s be the speed of the train. When the train moves towards the detector, the observed frequency f_L, towards = 3148 Hz. f_L, towards = f_s ( (v)/(v - v_s) ) 3148 = f_s ( (340)/(340 - v_s) ) (1) When the train moves away from the detector, the observed frequency f_L, away = 2073 Hz. f_L, away = f_s ( (v)/(v + v_s) ) 2073 = f_s ( (340)/(340 + v_s) ) (2) Divide equation (1) by equation (2): (3148)/(2073) = (f_s ( 340)/(340 - v_s) )f_s ( (340)/(340 + v_s) ) (3148)/(2073) = (340 + v_s)/(340 - v_s) 3148(340 - v_s) = 2073(340 + v_s) 1070320 - 3148v_s = 704820 + 2073v_s 1070320 - 704820 = 2073v_s + 3148v_s 365500 = 5221v_s v_s = (365500)/(5221) v_s ≈ 70.0057 m/s The speed of the train is approximately 70.01 m/s. Step 4: Calculate time t_1 (6.4). The detector started recording when the train was 350 m away. Time t_1 is when the train passes the detector, meaning it has covered the 350 m distance. Using the formula for constant speed: distance = speed × time. time = distancespeed t_1 = 350 m70.0057 m/s t_1 ≈ 4.9995 s Time t_1 is approximately 5.00 s. Last free one today — make it count tomorrow, or type /upgrade for unlimited.