Respuesta :
Answer:
Explanation:
mass of string = .0125 / 9.8
= 1.275 x 10⁻³ kg
Length of string l = 1.5 m .
m = mass per unit length
= ( .1.275 / 1.5) x 10⁻³ kg/m
m = .85 x 10⁻³ kg/m
wave equation: y(x,t) = (8.50 mm)cos(172 rad/m x − 4830 rad/s t)
compare with equation of wave
y(x,t) = Acos(K x − ω t)
ω ( angular velocity ) = 4830 rad/s
k = 172 rad/m
Velocity = ω / k
= 4830/172 m /s
= 28.08 m /s
velocity of wave = [tex]\sqrt{\frac{W}{m } }[/tex]
28.08 = [tex]\sqrt{\frac{W}{.85\times10^{-3} } }[/tex]
788.48 = W / .85 X 10⁻³
W = 670 x 10⁻³ N .
c ) wave length
wave length =2π / k
= 2 x 3.14 / 172
= .0365 m
no of wave lengths over whole length of string
= 1.5 / .0365
= 41
d )
equation for waves traveling down the string
= (8.50 mm)cos(172 rad/m x + 4830 rad/s t)
For the string, which tied to the ceiling at its upper end support a weight has,
- (a) Time does it take a pulse to travel the full length of the string is 0.0534 seconds.
- (b) The weight W is 0.67 N.
- (c) Number of wavelengths are on the string at any instant of time is 41.
- (d) The equation for waves traveling down the string is,
[tex]\rm y(x,t) = (8.50 mm)cos(172x rad/m - 4830t rad/s \;)[/tex]
What is equation of motion of standing wave?
The equation of the motion of standing wave can be given as,
[tex]\rm y(x,t) = Acos(kx-\omega t)[/tex]
Here, (k) is the wave number and ([tex]\omega[/tex]) is the angular velocity.
A 1.50-m string of weight 0.0125 N is tied to the ceiling at its upper end, and the lower end supports a weight W.
- (a) Time does it take a pulse to travel the full length of the string-
When you pluck the string slightly, the waves traveling up the string obey the equation:
[tex]y(x,t) = (8.50 )\cos(172x -4830)[/tex]
Compare this equation with the general equation of the motion of standing wave, we get,
Angular velocity ([tex]\omega[/tex]) is 4830 rad/s and the wave number (k) is 172 rad/m.
Now the velocity is the ratio of angular velocity to the wave number. Thus, velocity is,
[tex]v=\dfrac{\omega}{k}\\v=\dfrac{4830}{172}\\v=28.08\rm m/s[/tex]
The length of the string is 1.50 m. Thus, time does it take a pulse to travel the full length of the string is,
[tex]t=\dfrac{1.05}{28.08}\\t=0.0534\rm s[/tex]
- (b) The weight W-
For the string, force can be given as,
[tex]F=\dfrac{v^2}{\mu}\\F=\dfrac{28.08^2}{0.85\times10^{-3}}\\F=0.67\rm N[/tex]
- (c) Wavelengths are on the string at any instant of time-
The wavelength of the wave is twice the ratio of pi to the wave number.Thus, the wavelength is,
[tex]\lambda=\dfrac{2\times \pi}{k}\\\lambda=\dfrac{2\times \pi}{172}\\\lambda=0.0365\rm m[/tex]
As the length of the string is 1.50 m. Thus, number of wavelengths are on the string at any instant of time is,
[tex]\lambda=\dfrac{1.5}{0.0365}\\\lambda=41[/tex]
- (d) The equation for waves traveling down the string-
The equation can be given as,
[tex]\rm y(x,t) = (8.50 mm)cos(172x rad/m - 4830t rad/s \;)[/tex]
Thus, for the string, which tied to the ceiling at its upper end support a weight has,
- (a) Time does it take a pulse to travel the full length of the string is 0.0534 seconds.
- (b) The weight W is 0.67 N.
- (c) Number of wavelengths are on the string at any instant of time is 41.
- (d) The equation for waves traveling down the string is,
[tex]\rm y(x,t) = (8.50 mm)cos(172x rad/m - 4830t rad/s \;)[/tex]
Learn more about the equation of motion of standing wave here;
https://brainly.com/question/23236599
