Question

Determine the speed, frequency, period, wavelength, and amplitude of Wave A.

Answer 1

Given:

Waves A, B, and C travel 12.0 meters in 2.0 seconds through the given medium.

To find:

The speed, frequency, period, wavelength, and amplitude of wave A.

Step-by-step explanation:

As the wave covers a distance of 12 m in 2 seconds, the speed "v" of the wave can be calculated as:

`v=(d)/(t)`

Here, d is the distance covered by the wave and t is the time required to cover the distance.

Substituting the d = 12 m and t = 2 s in the above equation, we get:

`v=\frac{12\text{ m}}{2\text{ s}}=6\text{ m/s}`

The speed of the wave A is 6 m/s.

The frequency of a wave is defined as the number of wave cycles occurring per second.

From the above graph, we observe that there are a total of four wave cycles occurring in 2 s. Thus, the frequency of wave A can be calculated as:

`f=(N)/(t)`

Here, f is the frequency of the wave, N is the number of times the wave occurs and t is the time.

Substituting N = 4 and t = 2 s in the above equation, we get:

`f=\frac{4}{2\text{ s}}=2\text{ Hz}`

The frequency of wave A is 2 Hz.

The period "T" of the wave is related to the frequency "f" as:

`T=(1)/(f)`

Substituting the values in the above equation, we get:

`T=\frac{1}{2\text{ Hz}}=0.5\text{ s}`

The period of wave A is 0.5 s.

The wavelength λ of the wave is related to its speed "v" and frequency "f" as:

`\begin{gathered} v=f\lambda \\ \\ \lambda=(v)/(f) \end{gathered}`

Substituting the values in the above equation, we get:

`\lambda=\frac{6\text{ m/s}}{2\text{ Hz}}=3\text{ m}`

The wavelength of wave A is 3 m.

The amplitude of the wave is the maximum distance or displacement of the point on a vibrating body measured from the equilibrium position. Thus, from the given graph, we observe that the amplitude of wave A is 2 m.

Final answer:

The speed of wave A is 6 m/s.

The frequency of wave A is 2 Hz.

The time period of wave A is 0.5 s.

The wavelength of wave A is 3 m.

The amplitude of wave A is 2 m.