Question

sinusoidal water waves are generated in a large ripple tank. the waves travel at 20cm/s and their adjacent crests are 5cm apart. the time required for each new whole cycle to be generated is?

Answer 1

Answer:

1hour

Explanation:

1x*5=3*23426 and bro like

Answer 2

Answer:

The time required for each new cycle is the Time period of the wave and the value is 0.25s.

Explanation:

Sinusoidal Waves:

• Sinusoidal waves are in the form of periodic crests and troughs.
• A single wave consists of a crest and a trough.
• The distance between two consecutive crests or troughs is called the wavelength of the wave. It is denoted by $\lambda$.
• The number of waves passing a fixed point is called the frequency of the wave and is denoted by $\nu$.
• The time taker by the wave to complete one full cycle is called the time period, which is denoted by T. The relation between frequency and time period is given by

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

• The velocity of propagation of the wave is given by

                                                     $v=\nu\lambda$

Step 1:

Given the distance between adjacent crests to be 5cm, which is the wavelength of the wave and the velocity of propagation is 20cm/s.

                                                 $\lambda=5cm\\v=20cm/s$

Step 2:

Using the relation between velocity. wavelength and frequency of the wave we can write,

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

Step 3:

Substituting the values in the equation mentioned above, we have,

                                              $\nu=\frac{20}{5}\\ \nu=4Hz$

Step 4:

We are required to find the time required for each new whole cycle which is nothing but the time period of the wave. Using the relation between frequency and time period,

                                            $T=\frac{1}{\nu}\\T=\frac{1}{4}=0.25s$

Therefore, the time required for each new whole cycle is 0.25s