91Ó°ÊÓ

The number of vibrations per second is how frequency is defined. Wavelength is the shortest distance over which a wave can recur. The velocity of a wave is its speed over a certain period of time.

The speed of sound wave in water is 1480 m/s and the range of audible sound frequency is $20.0\mathrm{Hz}-20.0\mathrm{kHz}$.

Formula to calculate the shorter wavelength of the wave which is the distance between two blue dots on the wave pattern,

_{${\mathrm{λ}}_2=\frac{\mathrm{v}}{{\mathrm{f}}_2}$}

Here ${\mathrm{λ}}_2$is the shorter wavelength of wave in water, v is the speed of sound in air, and ${\mathrm{f}}_2$is the longer frequency.

Substitute 1480 m/s for v and 20 kHz for ${\mathrm{f}}_2$in the above equation.

_{$$\begin{gathered} {\mathrm{λ}}_2=\frac{1480\mathrm{m}/\mathrm{s}}{20\mathrm{kHz}} \\ =\frac{1480\mathrm{m}/\mathrm{s}}{\left(20\mathrm{kHz}\right)\left({\displaystyle \frac{{10}^3\mathrm{Hz}}{\mathrm{kHz}}}\right)} \\ =0.074\mathrm{m} \end{gathered}$$}

Therefore, the separation distance between two blue dots for shorter wavelength is $0.074\mathrm{m}$.

A measure stick is useful for measuring distances in the order of centimeters or a few meters, but it is not useful for measuring distances in the tens and hundreds of meters. The separation distance between red dots in water is in the tens of meters, or a very big value in centimeters, which is difficult to measure with a meter stick, whereas the separation distance between blue dots in water is in the centimeters, which is readily measured with a meter stick.

Therefore, the separation distance between red dots in water can be measured but not conveniently while the separation distance of blue dots in water can be conveniently measured by using a meter stick.