Chapter 13. Pressure variation for a sinusoidal sound wave propagating in the +x direction (13-9)

Question

8Cp20FnpfddOhYTcOwHw43hmNiKGd96BBc04LqVwTi3jgQ8m+08NjKyNmeWuyZCxpvnpk6aT85sQvAMA53O/jUaZDglchYsuEUwfUMhTAY4UuFJuCHf6qQ==
{"title":"IM: Pressure variation for a sinusoidal sound 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\":\"29,11,54,31\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Wrong","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"171,5,182,31\"}]"} {"title":"Phase angle","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"265,10,284,32\"}]"} {"title":"Angular frequency of the wave = 2 pi f","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"221,11,240,29\"}]"} {"title":"Pressure amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"80,12,97,35\"}]"}

Question

BJ+q/omwYbfH42VnQbIRxeXEzDGUd8idderrGz4Ji2CGlqqIcrDLSA0PfApTDShUn0GEViofjJQ=
{"title":"IM: Pressure variation for a sinusoidal sound 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\":\"29,11,54,31\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Correct!","type":"correct","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"171,5,182,31\"}]"} {"title":"Phase angle","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"265,10,284,32\"}]"} {"title":"Angular frequency of the wave = 2 pi f","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"221,11,240,29\"}]"} {"title":"Pressure amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"80,12,97,35\"}]"}

Question

BSm/p8ry4dYXtQ3h1a9oSg==
{"title":"IM: Pressure variation for a sinusoidal sound 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\":\"29,11,54,31\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Incorrect","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"171,5,182,31\"}]"} {"title":"Phase angle","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"265,10,284,32\"}]"} {"title":"Angular frequency of the wave = 2 pi f","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"221,11,240,29\"}]"} {"title":"Pressure amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"80,12,97,35\"}]"}

Question

d6HYmM9PCuRly8U45YA3yj5mAmM8IAsZIatkXHPQ/S+cAjwKyaWhETKgjGWud1rN
{"title":"IM: Pressure variation for a sinusoidal sound 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\":\"29,11,54,31\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Incorrect","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"171,5,182,31\"}]"} {"title":"Phase angle","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"265,10,284,32\"}]"} {"title":"Angular frequency of the wave = 2 pi f","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"221,11,240,29\"}]"} {"title":"Pressure amplitude of the wave","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"80,12,97,35\"}]"}

Question

Ap6azLKG6ZHKJGDGmPpVNX8ugQ3XLX8/+PM4WnRJ98KnBvCb
{"title":"IM: Pressure variation for a sinusoidal sound 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\":\"29,11,54,31\"}]"} {"title":"Angular wave number of the wave = 2pi / lambda","description":"Incorrect","type":"incorrect","color":"#993300","code":"[{\"shape\":\"rect\",\"coords\":\"171,5,182,31\"}]"} {"title":"Phase angle","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"265,10,284,32\"}]"} {"title":"Angular frequency of the wave = 2 pi f","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"221,11,240,29\"}]"} {"title":"Pressure amplitude of the wave","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"80,12,97,35\"}]"}

Review

Since a sound wave is a longitudinal wave, a positive value of \(y(x,t)\) means that the medium is displaced in the positive \(x\) direction, while a negative value of \(y(x,t)\) means that the medium is displaced in the negative \(x\) direction (Figure 13-9). As a result, as a sound wave propagates it squeezes together air molecules at some places along the wave, resulting in regions of air that have higher density and higher pressure. Adjacent regions of air are slightly depleted of air molecules and therefore have lower density and lower pressure. As Figure 13-9 shows, the pressure is greatest or least at points where the displacement is \(\textit{zero}\). So while the pressure is also described by a sinusoidal function, it is shifted by one quarter-cycle from the wave function for displacement \(y(x,t)\). That’s why we’ve drawn the displacement graph in Figure 13-9 as a \(\textit{cosine}\) curve but the pressure variation graph as a sine curve. In particular, if the displacement is described by Equation 13-6,

\(y(x,t) = A \cos\ (kx - \omega{t} + \phi)\)

the pressure variation is given by