Okay, so they want to basically Increase their grip, and they are taking advantage of the force of friction
To develop this problem it is necessary to apply the concepts related to Wavelength, The relationship between speed, voltage and linear density as well as frequency. By definition the speed as a function of the tension and the linear density is given by
![V = \sqrt{\frac{T}{\rho}}](https://tex.z-dn.net/?f=V%20%3D%20%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Crho%7D%7D)
Where,
T = Tension
Linear density
Our data are given by
Tension , T = 70 N
Linear density , ![\rho = 0.7 kg/m](https://tex.z-dn.net/?f=%5Crho%20%3D%200.7%20kg%2Fm)
Amplitude , A = 7 cm = 0.07 m
Period , t = 0.35 s
Replacing our values,
![V = \sqrt{\frac{T}{\rho}}](https://tex.z-dn.net/?f=V%20%3D%20%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Crho%7D%7D)
![V = \sqrt{\frac{70}{0.7}](https://tex.z-dn.net/?f=V%20%3D%20%5Csqrt%7B%5Cfrac%7B70%7D%7B0.7%7D)
![V = 10m/s](https://tex.z-dn.net/?f=V%20%3D%2010m%2Fs)
Speed can also be expressed as
![V = \lambda f](https://tex.z-dn.net/?f=V%20%3D%20%5Clambda%20f)
Re-arrange to find \lambda
![\lambda = \frac{V}{f}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7BV%7D%7Bf%7D)
Where,
f = Frequency,
Which is also described in function of the Period as,
![f = \frac{1}{T}](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7BT%7D)
![f = \frac{1}{0.35}](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B0.35%7D)
![f = 2.86 Hz](https://tex.z-dn.net/?f=f%20%3D%202.86%20Hz)
Therefore replacing to find ![\lambda](https://tex.z-dn.net/?f=%5Clambda)
![\lambda = \frac{10}{2.86}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B10%7D%7B2.86%7D)
![\lambda = 3.49m](https://tex.z-dn.net/?f=%5Clambda%20%3D%203.49m)
Therefore the wavelength of the waves created in the string is 3.49m
Power can be calculate through the equation,
Power = Force x velocity
It should be noted that velocity is calculated by dividing displacement by time. Thus, from the given in this item we can calculate for the power.
Power = (120 lb) x (12 ft/9 s)
<em> </em><span><em>Power = 160 lb.ft/s</em></span>
The formula for the period of wave is: wave period is equals to 1 over the frequency.
![waveperiod=\frac{1}{frequency}](https://tex.z-dn.net/?f=%20waveperiod%3D%5Cfrac%7B1%7D%7Bfrequency%7D%20)
To get the value of period of wave you need to divide 1 by 200 Hz. However, beforehand, you have to convert 200 Hz to cycles per second. So that would be, 200 cyles per second or 200/s.
By then, you can start the computation by dividing 1 by 200/s. Since 200/s is in fractional form, you have to find its reciprocal form and multiply it to one which would give you 1 (one) second over 200. This would then lead us to the value
0.005 seconds as the wave period.
wave period= 1/200 Hz
Convert Hz to cycles per second first
200 Hz x 1/s= 200/second
Make 200/second as your divisor, so:
wave period= 1/ 200/s
get the reciprocal form of 200/s which is s/200
then you can start the actual computation:
wave period= 1 x s divided by 200
this would give us an answer of
0.005 s.