Chapter 14, Problem 64A

(a)

To determine

The speed of the water waves in a lake.

Answer to Problem 64A

The speed of the water wave in a lake is $1.9\text{m/s}$ .

Explanation of Solution

Given:

Distance travelled by the water waveis $3.4\text{m}$ .

Time elapsed is $1.8\text{s}$ .

Period of oscillations is $1.1\text{s}$ .

Formula used:

  $v=\frac{d}{t}$

Where,

  $v$ : Velocity

  $t$ : Time

  $d$ : Distance

Calculation:

Calculate the speed of water:

  $v=\frac{d}{t}$

Substitute the values and solve:

  $v=\frac{3.4}{1.8}=1.9\text{m/s}$

Conclusion:

Hence, the speed of water wave in a lake is $v=1.9\text{m/s}$ .

(b)

To determine

The wavelength of water wave.

Answer to Problem 64A

  $\lambda =2.1\text{m}$

Explanation of Solution

Given:

Period of oscillations, $T=1.1\text{s}$ .

The speed of water wave in a lake is $v=1.9\text{m/s}$ .

Formula used:

  $\lambda =v\times T$

Where,

  $\lambda$ : Wavelength

  $v$ : Velocity

  $t$ : period

Calculation:

Substitute all the given values in the formula:

  $\lambda =v\times T$

  $v=\left(1.9\right)\times \left(1.1\right)$

  $\lambda =2.1\text{m}$

Conclusion:

Hence, the wavelength of water wave in the lake is $\lambda =2.1\text{m}$ .