2. Traveling transverse waves [1] In Eng. Phys. I (this subject), a traveling transverse wave is...

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2. Traveling transverse waves [1] In Eng. Phys. I (this subject), a traveling transverse wave is expressed as y1 = ym sin (kx-@t) ... (wave 1). What are the following quantities called? (a) y (b) ym (c) k (d) @ [2] (a) Show relation between k and wavelength 2. (b) Show relation between @ and frequency f. (b) Show relation between and wave speed v. [3] (a) Show a mathematical form of a displacement of a traveling transverse wave y which has a phase difference with wave 1. The other parameters ym, k, w are the same with the wave 1. (b) Find the form of a resultant wave y'= y + y2. [4] (a) Show a mathematical form of a displacement of a transverse wave y3 which is the same with the wave 1 except traveling in the opposite direction. (b) Find the form of a resultant wave y" = y+y3. (c) Draw a figure of the resultant wave y" as a function of position x. [5] (a) On a string stretched between two clamps, describe a requirement to generate standing wave (fundamental mode) with using a sketch of the string. (b) Draw the string with the third harmonic. Moreover, add "arrow(s) ()" at position(s) of "node". 2. Traveling transverse waves [1] In Eng. Phys. I (this subject), a traveling transverse wave is expressed as y1 = ym sin (kx-@t) ... (wave 1). What are the following quantities called? (a) y (b) ym (c) k (d) @ [2] (a) Show relation between k and wavelength 2. (b) Show relation between @ and frequency f. (b) Show relation between and wave speed v. [3] (a) Show a mathematical form of a displacement of a traveling transverse wave y which has a phase difference with wave 1. The other parameters ym, k, w are the same with the wave 1. (b) Find the form of a resultant wave y'= y + y2. [4] (a) Show a mathematical form of a displacement of a transverse wave y3 which is the same with the wave 1 except traveling in the opposite direction. (b) Find the form of a resultant wave y" = y+y3. (c) Draw a figure of the resultant wave y" as a function of position x. [5] (a) On a string stretched between two clamps, describe a requirement to generate standing wave (fundamental mode) with using a sketch of the string. (b) Draw the string with the third harmonic. Moreover, add "arrow(s) ()" at position(s) of "node".

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