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Chapter 2: Q7DQ (page 496)

Is it possible to have a longitudinal wave on a stretched string? Why or why not? Is it possible to have a transverse wave on a steel rod? Again, why or why not? If your answer is yes in either case, explain how you would create such a wave.

Short Answer

Expert verified

The production of a longitudinal wave in a stretched string is not achievable. This is due to the string being very hard to compress throughout its length. A transverse wave will result from its bending.

A steel rod may produce transverse waves because steel has form flexibility.

Step by step solution

01

Concept of a longitudinal and transverse wave.

The medium moves in parallel with the direction of longitudinal waves. Transverse waves, on the other hand, force the medium to travel perpendicular to the direction of the wave.

02

Longitudinal wave relation with stretched string

It is impossible to compress a stretched string. A longitudinal wave can propagate across a medium that is alternately compressed and rarefied. Therefore, with a stretched string, a longitudinal wave is not feasible. The crests and troughs of longitudinal waves alternate. Pressure waves are another name for them. Stretching a string will cause a longitudinal wave to bend and create a transverse wave. Therefore, with a stretched string, longitudinal waves are not achievable.

Therefore, transverse waves can propagate through a stretched string

03

Transverse wave relation with steel rod

For a Transverse wave to propagate the medium must be elastic. Steel is an Elastic material. It has a considerable amount of Elasticity.

Therefore, a transverse wave can pass through the steel rod.

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Consider a sound wave in air that has displacement amplitude 0.0200 mm. Calculate the pressure amplitude for frequencies of (a) 150 Hz; (b) 1500 Hz; (c) 15,000 Hz. In each case compare the result to the pain threshold, which is 30 Pa.

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(b) Use \(y\left( {x,t} \right)\) to find an expression for the transverse velocity \({v_y}\)of a particle in the string on which the wave travels. (c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed \(v\) ? Less than\(v\)? Greater than\(v\)?
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