Question

What are the amplitude, frequency, and wavelength of the wave in the given figure?

Short answer

Part (a) The amplitude of the wave is 6cm.

Part (b) The frequency of the wave is 1.67 Hz.

Part (c) The wavelength is 1.2 m.

Step-by-step solution

Part (a) Step 1. Given information

From the given graph:

The wave is periodic.

The time period is given as T=0.6s

The velocity of the wave is given as v= 2m/s.

Part (a) Step 2. Calculating the Amplitude:

A history graph shows the wave’s displacement as a function of time at a single point in space.

Amplitude is defined as the maximum displacement from its equilibrium position.

From the graph , the amplitude(A) is 6cm

$A=6cm$

Part (b) Step 1. Calculating the frequency:

Frequency is defined as the number of complete waves in unit second.

It is the inverse of time period.

$T=\frac{1}{f}$

Substitute 0.6 s for T to calculate f.

$$\begin{gathered} f=\frac{1}{0.6s} \\ =1.67Hz \end{gathered}$$

Therefore, the frequency of the wave is 1.67 Hz.

Part (c) Step 1. Calculating the wavelength:

The distance between consecutive crests or troughs of an wave is called as the wavelength.

The formula to calculate the wavelength in terms of velocity in a periodic wave is given as

$\lambda =\frac{v}{f}$

Substitute 2 m/s for v and 1.67 Hz for f to calculate the wavelength.

$$\begin{gathered} \lambda =\frac{2m/s}{1.67Hz} \\ =1.2m \end{gathered}$$

Therefore, the wavelength is 1.2 m.