A wave on a string has the formula y 0030sin055x 628t 3 what...

A wave on a string has the formula y = 0.030sin(0.55x - 62.8t + Ï€/3). What is the wavelength, frequency, period, phase constant, and speed of the wave? The string has a linear density Î¼ = 0.020 kg/m. What is the tension in the string? What is the rate of energy flow of the wave? Sketch the reference circle, the snapshot graph at t = 0, and the history graph at x = 0.

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Transcript

00:01 So let's extract the information from the given equation.

00:04 First of all, the wave number k from the given equation is there is 0 .55.

00:11 Radion per meter angular frequency omega equals 62 .8 by looking at the equation, radiance per second, and phi, that is simply equal to pi by three radiance.

00:27 Let's start from part a.

00:31 In part a, we have to find the lambda, there is wavelength.

00:38 Wave length is equal to 2 pi divided by k.

00:47 There is the wave number, right? simply 2 pi divided by the value of the k is 0 .55.

00:56 So from here the wavelength equals 11 .4 meters.

01:05 For part b we will go here.

01:08 In part b we have to find the frequency.

01:11 We know that frequency equals the angular frequency divided by 2 pi.

01:20 Angular frequency is given that equals 62 .8 radian per second divided by 2 pi.

01:26 From here frequency equals 10 hertz.

01:30 So in part c, we have to find the time period.

01:38 Time period is basically equal to the reciprocal of the frequency.