contestada

A wave pulse travels along a string at a speed of 200 cm/s. What will be the speed if:
a. The string’s tension is doubled?
b. The string’s mass is quadrupled (but its length is unchanged)?
c. The string’s length is quadrupled (but its mass is unchanged)?
d. The string’s mass and length are both quadrupled?
Note that parts a–d are independent and refer to changes made to the original string.

Respuesta :

Answer:

a) [tex] v_f = \sqrt{\frac{2TL}{m}} = \sqrt{2} v = \sqrt{2}2m/s =2.83 m/s [/tex]

The velocity increase by a factor of [tex]\sqrt{2}[/tex]

b) [tex] v_f = \sqrt{\frac{TL}{4m}} = \frac{1}{2} v = \frac{1}{2} *2m/s =1 m/s [/tex]

The velocity decrease by a factor of 2.

c) [tex] v_f = \sqrt{\frac{4TL}{m}} = 2} v = 2 *2m/s =4m/s [/tex]

The velocity increase by a factor of 2

d) [tex]v_f = \sqrt{\frac{4TL}{4m}} = v = 2m/s [/tex]

The velocity not changes.

Explanation:

For this case we know that the velocity is [tex] v = 200 cm/s = 2m/s[/tex]

[tex]v_f[/tex] represent the final velocity after the changes specified,

Part a

The formula for the speed of a wave in a string is given by:

[tex] v = \sqrt{\frac{T}{\rho}}[/tex]

And the linear density is defined as:

[tex] \rho = \frac{m}{L}[/tex]

And if we replace this we got:

[tex] v = \sqrt{\frac{TL}{m}}[/tex]

If the tension mass is doubled we have this:

[tex] v_f = \sqrt{\frac{2TL}{m}} = \sqrt{2} v = \sqrt{2}2m/s =2.83 m/s [/tex]

The velocity increase by a factor of [tex]\sqrt{2}[/tex]

Part b

If we mass is quadrupled we have this:

[tex] v_f = \sqrt{\frac{TL}{4m}} = \frac{1}{2} v = \frac{1}{2} *2m/s =1 m/s [/tex]

The velocity decrease by a factor of 2.

Part c

If the length is quadrupled we have this:

[tex] v_f = \sqrt{\frac{4TL}{m}} = 2} v = 2 *2m/s =4m/s [/tex]

The velocity increase by a factor of 2

Part d

For this case we know that the mass and the length are both quadrupled and we got:

[tex]v_f = \sqrt{\frac{4TL}{4m}} = v = 2m/s [/tex]

The velocity not changes.

Otras preguntas