Chapter 13. Wave function for a sinusoidal wave propagating in the +x direction (13-6)

Question

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{"title":"Wave function for a sinusoidal wave propagating in the +x direction","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"21,9,37,27\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Incorrect","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"163,2,179,25\"}]"} {"title":"Phase angle","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,296,30\"}]"} {"title":"Angular frequency of the wave = 2pi f","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"218,8,240,27\"}]"} {"title":"Amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"84,3,108,27\"}]"}

Question

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{"title":"Wave function for a sinusoidal wave propagating in the +x direction","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"21,9,37,27\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Correct!","type":"correct","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"163,2,179,25\"}]"} {"title":"Phase angle","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,296,30\"}]"} {"title":"Angular frequency of the wave = 2pi f","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"218,8,240,27\"}]"} {"title":"Amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"84,3,108,27\"}]"}

Question

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{"title":"Wave function for a sinusoidal wave propagating in the +x direction","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"21,9,37,27\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Wrong","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"163,2,179,25\"}]"} {"title":"Phase angle","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,296,30\"}]"} {"title":"Angular frequency of the wave = 2pi f","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"218,8,240,27\"}]"} {"title":"Amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"84,3,108,27\"}]"}

Question

d6HYmM9PCuRly8U45YA3yj5mAmM8IAsZIatkXHPQ/S+cAjwKyaWhETKgjGWud1rN
{"title":"Wave function for a sinusoidal wave propagating in the +x direction","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"21,9,37,27\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Wrong","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"163,2,179,25\"}]"} {"title":"Phase angle","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,296,30\"}]"} {"title":"Angular frequency of the wave = 2pi f","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"218,8,240,27\"}]"} {"title":"Amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"84,3,108,27\"}]"}

Question

jgsMRhUpiW7jFvmHQSbmgVK6asrJrCBreZ9vNQ==
{"title":"Wave function for a sinusoidal wave propagating in the +x direction","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"21,9,37,27\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Wrong","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"163,2,179,25\"}]"} {"title":"Phase angle","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,296,30\"}]"} {"title":"Angular frequency of the wave = 2pi f","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"218,8,240,27\"}]"} {"title":"Amplitude of the wave","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"84,3,108,27\"}]"}

Review

Since \(2\pi\) represents the number of radians in one cycle and wavelength \(\lambda\) is in meters, the angular wave number \(k\) is measured in radians per meter (rad/m). We use the adjective \(\textit{angular}\) since the term "wave number" is typically used for \(1/\lambda\), the reciprocal of the wavelength. This quantity multiplied by \(2\pi\) is the angular wave number \(k = 2\pi{f}\).

In terms of angular wave number, we can rewrite Equation 13-4 as