# Wave Equation Problems

1. Two waves are traveling through the same container of nitrogen gas. Wave A has a

wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be________ the speed of wave A.

a. one-ninth

b. one-third

c. the same as

d. three times larger than

2. As the wavelength of a wave in a uniform medium increases, its frequency will _____.

a. decrease

b. increase

c. remain the same

3. The speed of a wave depends upon (i.e., is causally effected by) ...

a) the properties of the medium through which the wave travels

b) the wavelength of the wave.

c) the frequency of the wave.

d) both the wavelength and the frequency of the wave.

https://brainmass.com/physics/properties/wave-equation-problems-87873

#### Solution Preview

1. The answer is C. The medium is the same for both of these waves ("the same container

of nitrogen gas"). Thus, the speed of the wave will be the same. Alterations in a

property of a wave (such as wavelength) will not ...

#### Solution Summary

Calculation of the speed of a wave through nitrogen gas. Relationship between wave speed, wave properties, and medium properties.

Dispersive Waves: Group and Phase Velocity Example Problem

Please see the attached file.

In some media, waves of different frequencies travel at different speeds. Such a medium is called a dispersive medium because waves that are not sinusoidal will change shape or disperse over time.

For example, a superposition of two such waves of different frequencies is described by the equation:

y(x,t) = cos(k1x - w1t) + cos(k2x - w2t)

Substitute into the equation above the following expressions for k1, k2, w1 and w2

And show that: (see attachment for equation)

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