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Chapter 16: Q19P (page 473)

What is the speed of a transverse wave in a rope of length2.00 mand mass60.0 gunder a tension of 500 N?

Short Answer

Expert verified

The speed of a transverse wave is 129.1 m/s

Step by step solution

01

The given data

  • The length of the rope,L=2.00 m.
  • The tension in the rope, T=5.00 N
  • The mass of the rope,m =60.0 g=0.0600 kg
02

Understanding the concept of linear density

The mass per unit length of the wire is known as the linear density of the wire.

By finding the linear mass density of the rope, we can find the speed of the wave.

The wave speed in terms of tension and linear density,

v=tμ …..(i)

The linear density of a body,

μ=mL …..(ii)

03

Calculation of the speed of the transverse wave

The linear mass density μof the rope using equation (ii) and the given values can be given as:

μ=0.0600kg2.00m=0.0300kg/m

Thus, the wave speed using equation (i) is given as:

v=500N0.0300kg/m=129.1m/s

Hence, the value of the speed of the transverse wave is 129.1 m/s

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Most popular questions from this chapter

In Figure 16-36 (a), string 1 has a linear density of 3.00 g/m, and string 2 has a linear density of 5.00 g/m. They are under tension due to the hanging block of mass M = 500 g. (a)Calculate the wave speed on string 1 and (b) Calculate the wave speed on string 2. (Hint:When a string loops halfway around a pulley, it pulls on the pulley with a net force that is twice the tension in the string.) Next the block is divided into two blocks (with M1+M2=M) and the apparatus is rearranged as shown in Figure (b). (c) Find M1and (d) Find M2such that the wave speeds in the two strings are equal.

The following two waves are sent in opposite directions on a horizontal string so as to create a standing wave in a vertical plane:

y1(x,t)=(6.00mm)sin(4.00πx-400πt)y2(x,t)=(6.00mm)sin(4.00πx+400πt)

within X meters andin seconds. An antinode is located at point A. In the time interval that point takes to move from maximum upward displacement to maximum downward displacement, how far does each wave move along the string?

At timet = 0and at position x = 0 malong a string, a traveling sinusoidal wave with an angular frequency of 440 rad/shas displacement y=+4.5mmand transverse velocityu=0.75m/s . If the wave has the general formy(x,t)=ymsin(kx-ωt+ϕ) , what is phase constant ϕ?

A string along which waves can travel is2.70 mlong and has a mass of 260 g. The tension in the string is 36.0 N. What must be the frequency of traveling waves of amplitude 7.70 mmfor the average power to be 85.0 W?

A uniform rope of mass m and length L hangs from a ceiling.(a)Show that the speed of a transverse wave on the rope is a function of y, the distance from the lower end, and is given byv=gy .(b)Show that the time a transverse wave takes to travel the length of the rope is given byt=2L/g.
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