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A transverse sinusoidal wave on a wire is moving in the -x-direction. Its speed is 30.0 m/s, and its period is 16.0 ms. At t= 0, a colored mark on the wire at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.40 m/s. (a) What is the amplitude of the wave (in m)? 0.48 Write the standard form of the wave function for a wave travelling in the -x direction, then take the partial derivative with respect to time to find the velocity. Use your given values to write y and veransverse and apply the identity sin (w) + cos (w) = 1 to find A. You will also need to calculate o from the given values. Don't forget to convert units as needed m

A transverse sinusoidal wave on a wire is moving in the -x-direction. Its speed is 30.0 m/s, and its period is 16.0 ms. At t= 0, a colored mark on the wire at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.40 m/s. (a) What is the amplitude of the wave (in m)? 0.48 Write the standard form of the wave function for a wave travelling in the -x direction, then take the partial derivative with respect to time to find the velocity. Use your given values to write y and veransverse and apply the identity sin (w) + cos (w) = 1 to find A. You will also need to calculate o from the given values. Don't forget to convert units as needed m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A transverse sinusoidal wave on a wire is moving in the -x-direction. Its speed is 30.0 m/s, and its period is 16.0 ms. At t = 0, a colored mark on the wire at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.40 m/s. (a) What is the amplitude of the wave (in m)? 0.48 Write the standard form of the wave function for a wave travelling in the -x direction, then take the partial derivative with respect to time to find the velocity. Use your given values to write y and veransverse and apply the identity sin (@) + cos (w) = 1 to find A. You will also need to calculate o from the given values. Don't forget to convert units as needed. m (b) What is the phase constant (in rad)? 392.5 Use the expressions you wrote for y and vransverse from part (a), and divide them to find an equation for tan(@). Take the inverse to find p. Note that the angle you are looking for is in the second quadrant, so you will need to modify your calculator answer as needed. rad (c) What is the maximum transverse speed of the wire (in m/s)? 7.85 m/s (d) Write the wave function for the wave. (Use the form A sin(kx + ot + p). Assume that y and x are in m and t is in s. Do not include units in your answer.) y(x, t) = 7.85 Use the standard wave function and the value of A calculated in part (a) and w and o in part (b). You will need to calculate k, which you can do using the relationship among speed, frequency, and wavelength and the relationship between frequency and angular frequency. m Need Help? Read It
Transcribed Image Text:A transverse sinusoidal wave on a wire is moving in the -x-direction. Its speed is 30.0 m/s, and its period is 16.0 ms. At t = 0, a colored mark on the wire at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.40 m/s. (a) What is the amplitude of the wave (in m)? 0.48 Write the standard form of the wave function for a wave travelling in the -x direction, then take the partial derivative with respect to time to find the velocity. Use your given values to write y and veransverse and apply the identity sin (@) + cos (w) = 1 to find A. You will also need to calculate o from the given values. Don't forget to convert units as needed. m (b) What is the phase constant (in rad)? 392.5 Use the expressions you wrote for y and vransverse from part (a), and divide them to find an equation for tan(@). Take the inverse to find p. Note that the angle you are looking for is in the second quadrant, so you will need to modify your calculator answer as needed. rad (c) What is the maximum transverse speed of the wire (in m/s)? 7.85 m/s (d) Write the wave function for the wave. (Use the form A sin(kx + ot + p). Assume that y and x are in m and t is in s. Do not include units in your answer.) y(x, t) = 7.85 Use the standard wave function and the value of A calculated in part (a) and w and o in part (b). You will need to calculate k, which you can do using the relationship among speed, frequency, and wavelength and the relationship between frequency and angular frequency. m Need Help? Read It
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