Physics 131- Section L Thursdays 9:00 AM ILC S110 June 29, 2017 Abstract In this experiment we looked at the the frequencies of the string that can be controlled by the computer, that will create different nodes on the string as it vibrates so we are able to find the wavelength and average speed of the wave, also with the addition of different hanging weights and how that changes the values. Questions & Answers 1. A guitar string of 0.8 m has a standing wave with three anti-nodes (n=3). What is the wavelength of the standing wave along the string? Hint: Use Eq. 5.3 in the lab manual. (2 points) Equation of the wavelength: λn = 2L/ n so λn = 2(.8m)/3=.53m 2. If the guitar string is vibrating at a frequency of 432Hz, what is the speed of the standing wave? (2 points) The speed of a standing wave can be determined by speed = frequency • wavelength. We know the frequency is 432Hz, from question 1 we know the wavelength is .53 so 432Hz*.53m= 228.96m/s 3. For the each value of mass hanging on the string, make a table of your measurements of frequency and wavelength for the different values of anti-nodes n. For each value of n calculate the speed of the wave on the string. (2 points) 200g hanging mass n value Frequency (Hz) Wavelength (m) Speed (m/s) 1 23 .7 16.1 2 46 .35 16.1 3 69 .23 16.1 4 93 .175 16.285 117 .14 16.38 400g hanging mass n value Frequency (Hz) Wavelength (m) Speed (m/s) 1 33 .7 23.1 2 66 .35 23.1 3 99 .23 23.1 4 132 .175 23.1 5 165 .14 23.1 600g hanging mass n value Frequency (Hz) Wavelength (m) Speed (m/s) 1 40 .7 28 2 82 .35 28.7 3 123 .23 28.7 4 164 .175 28.7 5 204 .14 28.56 4. Does the speed of the wave change as the frequency changes? Why or why not? (2 points) No because an increase in wave frequency causes a decrease in wavelength, which keeps the speed of the wave proportional over time. Since the speed is determined by the wavelength and the frequency multiplied to one another. 5. What is the average and the standard deviation of the speed of the wave on the string? (2 points) The average can be determined by the equation Vavg=Sum Vn/5 The standard deviation can be determined by the equation sqrt(⅕*Sum(Vn-Vavg)2)For the 200g weight: Average: 16.191 m/s Standard Deviation: .1162 For the 400g weight Average:23.1 m/s Standard Deviation: 3.5527E-15 For the 600g weight Average: 28.532 m/s Standard Deviation: .2715 6. What happens to the speed of the wave when the mass hanging on the string is changed? Does it go up down or stay the same? Why? (2 point) The speed of the wave increases as the mass hanging on the string increases. Since the speed in equal to the square root of the tension divided by the constant mu, and tension is equal to gravity* the mass of the hanging object. Since the hanging mass is accounted for in the numerator, when the mass increases, the whole number increases. 7. Make a plot of the velocity of the string vs the tension of the string F. (2 points)’8. Compare the tension in the string to tuning a guitar string. If the tension in a guitar string is increased what happens to the pitch? How is the pitch related to the speed of the wave? (2 points) As the tension of the guitar increases, the pitch also increases because the pitch is the frequency. Pitch is related to the speed of the wave because the speed of the wave is determined by frequency (pitch)* wavelength. So as the pitch increases, the speed of the wave will increase because in the case of the guitar, the wavelength remains constant. Conclusion This lab let us see how changing the mass on the string, increased the frequency of the string which also increases the average speed. The wavelength remained constant because it is dependent on the nodes and length of the string while the average speed increased with the changing mass. It showed there is a proportional relationship between the mass and speed of the