11.1.3 A Wave on a Rope: Wave Speed

Question 1

A Wave on a Rope: Wave Speed

Answer 1

• Waves on a rope travel at the speed . To derive this formula, apply Newton’s second law to a wave pulse on a rope.
• You now have two formulas for wave speed:

Question 2

The derivation of the velocity of a transverse wave in a rope consists of analyzing an infinitesimal section of mass dm. The figure shows the various elements of the derivation. Based on the figure, which of the following relationships is not valid?

Answer 2

dl = Rd theta describes the length of the rope section

Question 3

How is the speed v of a transverse wave on a rope related to its density u?

Answer 3

v = 1/sqrt(u)

Question 4

The Term T represents _______

Answer 4

the tension in the rope

Question 5

To double the speed of a wave on a string, how would you adjust the tension and the density of the string?

Answer 5

• Quadruple the tension T.
• Decrease the density by 1/4.
• Double the tension and halve the density.

Question 6

Which of the following is the unit of tension, T, in a rope?

Answer 6

• N (newton)

- kg/m*s^2

Question 7

True or false?

Increasing the tension in a rope, while keeping the density constant, causes an increase in the speed of the wave.

Answer 7

true

Question 8

The velocity of a transverse wave on Rope 1 with fixed tension and density is 2m/s. The velocity of a wave on Rope 2 with the same tension as Rope 1 is 3m/s. Which of the following is the ration, u2/u1, between the density of the two ropes

Answer 8

4/9

Question 9

unit of u

Answer 9

kg / m

Question 10

The frequency of a wave on a rope is 2 cycles per second and its wavelength is 3m. The rope’s density is 0.1 kg/m. Which of the following is the tension in the rope?

Answer 10

T = 3.6 N