A string is stretched between two supports that are L = 1.2...

A string is stretched between two supports that are L = 1.2 m apart. It resonates at a frequency of f = 450 Hz with a standing wave pattern that has two nodes between the two supports. 1) Find the wavelength (lambda) in meters. 2) Suppose that the tension, T, in the string is increased by a factor of 4. What is the new frequency, f', in unit of Hz, if the string vibrates with the same standing wave pattern that it began with (i.e. A standing wave pattern that has two nodes between the supports). 3) Find the velocity, v, of the wave in part 2. 4) Find the density of the string ((mu)) in kg/m if the Tension from part 2 is 720 N.

Transcript

00:01 Hello students in this question, a standing wave which is produced by a particular string thrust between two supports are been shown in the figure where it is given that the distance between the supports capital letter l is taken to be 1 .2 meter initial frequency of the string f0 is taken to be 450 heads.

00:23 Now in the first part of the question we need to find out the wavelength of this particular wave which is taken as lambda.

00:32 And here we can say that for the case of standing waves, the total distance between the nodes can be taken as capital letter l to be equal to n into lambda divided by 2.

00:43 And from the figure given here we get the value of number of nodes n to be equal to a value of 3.

00:49 By substituting the value of l and n in the above equation, our equation changes as 1 .2 to be 3 into lambda divided by 2, which on simplification gives the value of wavelength of the wave lambda to be equal to 0 .8 meter.

01:08 Now in the second part of the question, we need to find out the new frequency of this wave which is taken as f -dash.

01:15 And here it is given that the initial tension of the string is taken as capital -ed -t and the new tension is taken as t -dash which will be equal to 4 times the value of initial tension capital t.

01:28 Now the equation of velocity of a standing wave is taken as small letter v to be equal to square root the value of tension of the string capital letter t divided by linear mass density which is taken as mu.

01:42 And the equation of frequency is taken as frequency f to be equal to velocity v divided by wavelength lambda.

01:50 Now we substitute in the equation of b and lambda in this equation we get the equation of frequency of frequency as f to be equal to 3 divided by 2 into capital letter l into square root the value of tension force capitalator t divided by mu...

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