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
Here are the solutions to Question 3. 3.1 State the Doppler Effect in words. The Doppler Effect is the apparent change in the frequency (and thus pitch) of a wave observed when the source of the wave and the observer are moving relative to each other. The frequency increases when they move closer and decreases when they move apart. 3.2 Determine the period of the detected wave. Step 1: Identify the time for half a period from the graph. The graph shows a peak at t = 3.5 × 10^-4 s and a trough at t = 10.5 × 10^-4 s. The time difference between a peak and a trough is half a period (T/2). (T)/(2) = (10.5 - 3.5) × 10^-4 s (T)/(2) = 7.0 × 10^-4 s Step 2: Calculate the full period (T). T = 2 × 7.0 × 10^-4 s T = 14.0 × 10^-4 s T = 0.0014 s The period of the detected wave is 1.40 × 10^-3 s. 3.3 Calculate the frequency of the detected sound wave. Step 1: Use the relationship between frequency (f) and period (T). f = (1)/(T) Step 2: Substitute the period calculated in 3.2. f = (1)/(14.0 × 10^-4) s f = (10000)/(14) Hz f = (5000)/(7) Hz f ≈ 714.29 Hz The frequency of the detected sound wave is 714 Hz. 3.4 Calculate the speed of the moving car. Step 1: Identify the given values. Source frequency, f_s = 600 Hz Speed of sound in air, v = 340 m/s Detected frequency, f_L = 714.29 Hz (using the more precise fraction (5000)/(7) Hz for calculation) Step 2: Determine the appropriate Doppler Effect formula. Since the detected frequency (f_L = 714.29 Hz) is higher than the source frequency (f_s = 600 Hz), the car (source) must be moving towards the stationary listener. The formula for a moving source and stationary listener approaching each other is: f_L = f_s ( (v)/(v - v_s) ) where v_s is the speed of the source (car). Step 3: Rearrange the formula to solve for v_s. (f_L)/(f_s) = (v)/(v - v_s) f_L (v - v_s) = f_s v f_L v - f_L v_s = f_s v f_L v_s = f_L v - f_s v v_s = v ( (f_L - f_s)/(f_L) ) Step 4: Substitute the values and calculate v_s. v_s = 340 m/s ( (5000)/(7) Hz - 600 Hz(5000)/(7) Hz ) v_s = 340 m/s ( (5000 - 4200)/(7)(5000)/(7) ) v_s = 340 m/s ( (800)/(7)(5000)/(7) ) v_s = 340 m/s ( (800)/(5000) ) v_s = 340 m/s ( (8)/(50) ) v_s = 340 m/s ( (4)/(25) ) v_s = (1360)/(25) m/s v_s = 54.4 m/s The speed of the moving car is 54.4 m/s. 3 done, 2 left today. You're making progress.