Question

When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 75-cm-wide tub is 0.85 Hz. What is the speed of the water wave?

Short answer

The speed of water wave is $1.275\mathrm{m}/\mathrm{s}$.

Step-by-step solution

Determination of the speed of the water wave

The wave speed is measured by using the correlation among frequency as well as wavelength. In this case, the wavelength is two times the length of the pool.

Given data

The length of the pool is $l=75\mathrm{c}\mathrm{m}$.

The frequency of water wave is $f_1=0.85\mathrm{H}\mathrm{z}$.

Calculation of the wave speed

The wave speed is calculated as,

$\begin{array}{rl}l\nu & =\lambda \times f_1\\ \nu & =2\times l\times f_1\end{array}$

Here, $\lambda$ is the wavelength.

Substitute the known values in the above equation.

$\begin{array}{r}\nu =2\times \left(75\mathrm{c}\mathrm{m}\times \frac{1\mathrm{m}}{100\mathrm{c}\mathrm{m}}\right)\times 0.85\mathrm{H}\mathrm{z}\\ =1.275\mathrm{m}/\mathrm{s}\end{array}$

The wave speed is $1.275\mathrm{m}/\mathrm{s}$.