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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

A sinusoidal wave is traveling on a string with speed 40 cm/s. The displacement of the particles of the string at x = 10 cmvaries with time according to y = (5.0 cm) sin[1.0-4.0s-1t].The linear density of the string is 4.0 g/cm. (a)What is the frequency and (b) what is the wavelength of the wave? If the wave equation is of the form,y(x,t)=ymsin(kx±ωt) (c) What isym, (d) What is k, (e) What isω, and (f) What is the correct choice of sign in front ofω? (g)What is the tension in the string?

The tension in a wire clamped at both ends is doubled without appreciably changing the wire’s length between the clamps. What is the ratio of the new to the old wave speed for transverse waves traveling along this wire?

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.

String is stretched between two clamps separated by distance L . String B, with the same linear density and under the same tension as string A, is stretched between two clamps separated by distance 4L. Consider the first eight harmonics of stringB. For which of these eight harmonics of B(if any) does the frequency match the frequency of (a) A’s first harmonic, (b) A’s second harmonic, and (c)A’s third harmonic?

(a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the positive direction of a yaxis with an angular wave number of 60 cm-1, a period of 0.20 s, and an amplitude of 3.0 mm. Take the transverse direction to be thedirection. (b) What is the maximum transverse speed of a point on the cord?
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