Chapter 11, Problem 72GP

To determine

To Calculate: The speed of waves in the coffee.

Answer to Problem 72GP

The speed of waves in the coffee is $0.16\text{m/s}$ .

Explanation of Solution

Given Information:

The diameter of the cup of coffee, $\mathrm{d}=8\text{cm}$

Formula used:

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

Here, $\mathrm{v}$ is the speed of wave,

  $\mathrm{f}$ is the frequency of wave,

  $\mathrm{\lambda }$ is the wavelength of wave.

Calculation:

The cup can be related as tube with closed ends with length as cup’s diameter. So, wavelength of coffee wave is double the cup’s diameter.

  $\begin{array}{l}\mathrm{\lambda }=2\text{d}\\ \mathrm{\lambda }=16\text{cm}\end{array}$

From the above equation

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

According to question

1 step per second, so frequency, $\mathrm{f}=1\text{Hz}$

Then, $\mathrm{v}=(1\text{Hz})\times (0.16\text{m})$

  $\mathrm{v}=0.16\text{m/s}$

Conclusion:

The speed of waves in the coffee is $0.16\text{m/s}$ .