Properties of Waves

Properties of Waves PRE-LAB QUESTIONS 1. If a wave traveling through air decreases its wavelength by half, what happens to the wave speed and frequency? The wave speed will remain the same because the medium hasn’t changed, but because frequency is inversely proportional to wavelength, it will double because the wavelength decreased by half. 2. A transverse wave is traveling down a rope with mass, m = 10 kg, and length, L = 50 m. If the rope is under a tension force of 2,000 N, calculate the wave speed of the transverse wave. Show your work. μ= μ= m L 10 50 = 0.2kg/m √ v= T μ v= √ 2000N 0.2kg/ m = 100m/s 3. If a slinky has a mass of 0.5 kg and 100 loops, calculate the mass density (m/L) of a slinky that is stretched 5 m, but only 80 loops are stretched. Show your work. L=5 m× μ= 100 =6.25m 80 0.5kg 6.25m =0.08 kg/m 4. Cite one example when you have experienced the Doppler effect and explain how it represented this scientific principle. I experienced the Doppler effect during my driver’s lesson. As I took a turn, I moved the car slowly and the driver behind me got agitated, so he hooted. Th sound was loud at first but as I drove away, it started to fade. Th reason for this is because when I was closer to the car, the soundwaves were condensed and reached my ear faster and as I drove off, the waves became more spread out and reached my ear slower. EXPERIMENT 1: WAVES Data Sheet Table 1: Slinky® Measurements Slinky Mass (kg) 0.23 Number of Loops 44 Mass/Loop (kg/loop) 5.23 x 10-3 Length (m) 2 Table 2: Wave Time Measurements for Relaxed Slinky® Trial Time (s) 1 1.06 2 1.11 3 1.10 4 1.28 5 1.26 Tension Force (N) 0.5 Table 3: Wave Time Measurements for Increased Tension Slinky® Trial Time (s) 1 0.66 2 0.83 3 0.77 4 0.72 5 0.73 Tension Force (N) 1,0 Post-Lab Questions 1. Describe how the speed of the waves were affected by the changing amplitude and frequency. The frequency doesn’t affect the wave speed 2. Compare the speed of the longitudinal waves to the speed of the transverse waves. Explain your answer. The longitudinal waves were faster than the transverse waves because they move parallel to the ground while transverse waves move perpendicular to the ground. 3. Use data from Table 1 and Table 2 to calculate the average time it took for the wave to travel down and back. Use this time to calculate the average speed for the traveling wave on the Slinky® for both situations. Fill in Table 4 with your answers. Trial 1 1.06 + 1.11 + 1.10 + 1.28 + 1.26 =0.417s 5 Trial 2 0.66 + 0.83 + 0.77 + 0.72+ 0.73 =0.742s 5 Table 4: Slinky® Measurements Velocity from Stopwatch (m/s) Trial Velocity from Tension and Mass density (m/s) Percent Difference (%) 1 4.79 2.09 56.4% 2 2.69 2.95 8.81% v= 2m 0.417 ¿ 4.79m/s 5. Calculate the wave speed using the formula for transverse waves. Fill in Table 4 with your answers. √ v = 0.5N×2 m 0.23kg = 2.09m/s 6. Calculate a percent difference between your velocities and record them in Table 4. % difference = 4.79−2.09 ×100 4.79 56.4% 7. Identify two sources of error in the experiment that could explain any percent difference. EXPERIMENT 2: STANDING WAVES ON A SLINKY® Data Sheet Table 5: Period of Various Nodes for Resonant Waves Number of Nodes Time for 10 Periods (s) Period (s) Frequency (Hz) 2 5.73 0.573 1.75 3 5.49 0.549 1.82 4 4.66 0.466 2.15 5 3.50 0.350 2.86 Frequency: 1 0.573s ¿ 1.75Hz Post-Lab Questions 1. Identify a trend of the change in frequency from one standing wave to the next. As time decreases, the frequency increases. 2. Calculate the change in frequency from one standing wave to the next (for example, from two nodes to three nodes). Nodes 2 and 3: 1.82 -1.75= 0.07 Hz 3. How many nodes were you able to create for your standing wave in Step 7? EXPERIMENT 3: WAVE SPEED OF MICROWAVES Post-Lab Questions 1. What is the distance in centimeters of a melted marshmallow hot spot? In meters? The distance is 7cm and 0.7m. 2. Based on your measurement of the hot spot what is the wavelength of a microwave? Frequency = 2450Hz Wavelength is the distance between two corresponding points on a wave, so Wavelength = 2 x distance = 2 x 0.7 = 1.4 m 3. Calculate the wave speed of microwaves from the labeled frequency and your measured distance. v =fλ v =(2450Hz )(1.4m ) v =3450m/ s v = 3.45 x 103 4. Compute the percent error between the calculated speed with the speed of light (c = 3.0 x 108 m/s)? Is this close to the speed of light? Explain why or why not. 5. Why was it important to remove the turntable function? How might the results vary if the turn table was functional during the experiment? It could have caused unnecessary heating and displacement of the marshmallows. EXPERIMENT 4: THE DOPPLER EFFECT Post-Lab Questions 1. How did the waves in front of the object appear compared to the waves behind the object? Explain why they were different. The waves in front of the cup moved upwards and the waves behind the cup moved downwards. 2. Draw a conclusion about the effect of a moving source on the velocity of the waves in a medium? The wave velocity would increase if the sources moved in the same direction, and if it moved in the opposite direction, it would decrease. 3. How does the Doppler effect help explain why a car’s engine sounds different as the car approaches you compared to after it passes you? The sound frequency increases when the car is near you and decreases when it passes you. 4. The Doppler effect is present in light waves as well. Red light has a slower frequency than blue light. What can you hypothesize about the motion of a distant star that appears “redshifted” to astrophysicists? Redshift refers to when a star is moving away from our galaxy. It’s wavelength increases and rarefaction occurs, and that shifts it to the red side of the electromagnetic spectrum.