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Chapter 14: Problem 6

As a wave propagates on a stretched string, the string moves back and forth sideways. Is the string speed related to the wave speed? Explain.

Short Answer

Expert verified
No, the string speed is not related to the wave speed. The string speed refers to the speed of the particles of the string vibrating back and forth, whereas the wave speed refers to the speed at which the wave moves along the string.

Step by step solution

01

Understanding wave propagation

When a wave propagates along a stretched string, it moves by making the particles of the string vibrate back and forth. However, the speed of the wave refers to how fast the energy of the wave moves along the string, not how fast the individual particles of the string are moving.
02

Understanding string speed

String speed refers to how fast the particles of the string are moving. This speed can both be related to amplitude and wavelength of the wave - the distance the particles move when a wave passes is influenced by how much the string is displaced from equilibrium (amplitude), but also how quickly it goes through a full cycle depends on the frequency, which is related to the wavelength.
03

Analysis of the relationship

Although the motion of the particles, i.e., the string speed, can influence the wave's characteristics (such as the amplitude and wavelength), it does not determine the wave speed. The wave speed depends on the properties of the system, such as the tension and mass density of the string, and the wave type (frequency, wavelength etc). Therefore, the string speed is not directly related to the wave speed.

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Most popular questions from this chapter

When a \(340-\mathrm{g}\) spring is stretched to a total length of \(40 \mathrm{cm},\) it supports transverse waves propagating at \(4.5 \mathrm{m} / \mathrm{s} .\) When it's stretched to \(60 \mathrm{cm},\) the waves propagate at \(12 \mathrm{m} / \mathrm{s} .\) Find (a) the spring's unstretched length and (b) its spring constant.

You see an airplane \(5.2 \mathrm{km}\) straight overhead. Sound from the plane, however, seems to be coming from a point back along the plane's path at \(35^{\circ}\) to the vertical. What's the plane's speed, assuming an average sound speed of 330 ms?

Medical ultrasound uses frequencies on the order of \(10^{7} \mathrm{Hz}\), far above the range of the human ear. In what sense are these waves "sound"?

A 1.5 -m-long pipe has one end open. Among its possible standingwave frequencies is \(225 \mathrm{Hz} ;\) the next higher frequency is \(375 \mathrm{Hz}\) Find (a) the fundamental frequency and (b) the sound speed.

Show by differentiation and direct substitution that any function of the form \(y=f(x \pm v t)\) satisfies the wave equation (Equation 14.5 ).
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