Which of the following statements is not true of waves in general?a)It may be a function of time and space.b)For practical reasons, it must be finite in extent.c)It may be a function of time only.d)It may be sinusoidal or cosinusoidal.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Waves are an important concept in physics and engineering. They are a disturbance that travels through a medium, transferring energy without the transfer of matter. There are many types of waves, including electromagnetic waves, sound waves, and water waves. However, there are some statements about waves that are not true, and this question asks us to identify one of those statements.

False Statement:
c) It may be a function of time only.

Explanation:
This statement is not true because waves are not just a function of time. They are also a function of space. Waves are characterized by their wavelength, frequency, amplitude, and velocity, all of which depend on both time and space. For example, sound waves are a function of both time and space because they travel through air, which is a medium that has a specific physical structure. Similarly, electromagnetic waves are a function of both time and space because they travel through the electric and magnetic fields in a vacuum or in a material medium.

True Statements:
a) It may be a function of time and space.
b) For practical reasons, it must be finite in extent.
d) It may be sinusoidal or cosinusoidal.

Explanation:
a) Waves are a function of both time and space. This means that they vary in both space and time. The properties of waves, such as their wavelength and frequency, depend on both time and space.

b) Waves must be finite in extent for practical reasons. This means that waves cannot extend infinitely in space or time. In reality, waves are limited by the physical properties of the medium through which they travel.

d) Waves may be sinusoidal or cosinusoidal. This means that waves can be described mathematically using trigonometric functions such as sine and cosine. Sinusoidal waves are characterized by their frequency, amplitude, and phase, and they are commonly used to describe many types of waves, including sound waves and electromagnetic waves.

Answer

Waves are not only functions of time. That is, waves don't depend on time. The are other variables that waves are dependent on. One example is the angular velocity (w) is one example. As the angular velocity of a wave changes, it also changes. Another example is the phase of a wave. If a sinusoidal wave v = Vsin(w+phi), then phi is the phase and as it changes, it affects the magnitude of the wave.

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