Question

What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7?

Short answer

The amplitude of the wave is 4 cm, the frequency is 2 Hz and the phase constant is 30^o

Step-by-step solution

Step 1. Write the given information

The snapshot graph of the wave at time t = 0 sec is given.

The speed of the wave is v = 24m/s

Step 2. To analyze the graph

The wavelength is the distance covered by the wave in one cycle. From the graph, the wavelength of the wave can be determined easily. The distance covered in one cycle is 12cm

1. Amplitude: The maximum displacement of the wave from its mean position is called the amplitude of the wave. From the graph, the amplitude is 4 cm.
2. Wavelength:The wavelength is the distance covered by the wave in one cycle. From the graph, the distance covered in one cycle is 12cm, therefore, the wavelength is 12cm
3. Frequency:The number of cycles a wave completes in one second is called the frequency of the wave. The formula to obtain frequency is $f=\frac{v}{\lambda }$
   Substitute the known values,
   $f=\frac{24m/s}{12m}=2s^{-1}$
4. The phase constant of the wave describes the initial condition for the wave.

From the given snapshot, it can be observed that the wave is starting from the displacement of 2cm. The phase constant is $\frac{\pi }{6}$radians