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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=t渭 鈥�..(颈)

The linear density of a body,

渭=mL 鈥�..(颈颈)

03

Calculation of the speed of the transverse wave

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

渭=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

A stretched string has a mass per unit length of5.00 g/cmand a tension of 10.0N. A sinusoidal wave on this string has amplitude of 0.12mmand a frequency of 100 Hzand is traveling in the negative direction of an xaxis. If the wave equation is of the form y(x,t)=ymsin(kx卤蝇迟), (a)What is ym, (b)What is k , (c)What is 蝇, and (d)What is the correct choice of sign in front of 蝇?

A sinusoidal wave of frequency 500 Hzhas a speed of 350 m/s . (a)How far apart are two points that differ in phase by蟺/3rad ? (b)What is the phase difference between two displacements at a certain point at times 1.00 msapart?

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-蝇t+蠒) , what is phase constant 蠒?

A certain transverse sinusoidal wave of wavelength 20cmis moving in the positive direction of an xaxis. The transverse velocity of the particle at x = 0as a function of time is shown in Fig. 16-49, where the scale of the vertical axis is set by. What are the (a) wave speed, (b) amplitude, and (c) frequency? (d) Sketch the wave between x = 0and x = 20cm at t = 2.0 s.

A sinusoidal wave of angular frequency1200 rad/s and amplitude 3,00mmis sent along a cord with linear density 2.00 g/mand tension 1200 N. (a)What is the average rate at which energy is transported by the wave to the opposite end of the cord? (b)If, simultaneously, an identical wave travels along an adjacent, identical cord, what is the total average rate at which energy is transported to the opposite ends of the two cords by the waves?If, instead, those two waves are sent along the samecord simultaneously, what is the total average rate at which they transport energy When their phase difference is 0, (b)When their phase difference is (c) 0(d)0.4蟺rad, and (e) is蟺rad?
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