Question

Tsunami! On December 26, 2004 , a great earthquake occurred off the coast of Sumatra and triggered immense waves (tsunami) that killed some 200,000 people. Satellites observing these waves from space measured 800 km from one wave crest to the next and a period between waves of 1.0 hour . What was the speed of these waves in m/s and in km/hr? Does your answer help you understand why the waves caused such devastation?

Short answer

The speed of sound wave in m/s is 222.2 m/s and in km/hr is 799.9 km/hr .

Step-by-step solution

Concept of the speed of the wave.

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 the wave is given by

_{$\mathrm{v}=\frac{\mathrm{\lambda }}{\mathrm{T}}$}

Where,$\mathrm{\lambda }$is the wavelength of the wave, v is the speed of sound. T is the time period of wave.

To calculate speed of the sound wave.

The distance between one wave crest to another crest is $\mathrm{\lambda }=800\mathrm{km}$

The time required to complete waves is$\mathrm{T}=1.0\mathrm{hour}$

Formula to calculate the speed of the wave is

_{$\mathrm{v}=\frac{\mathrm{\lambda }}{\mathrm{T}}$}

Substitute 800 km for $\mathrm{\lambda }$and 1.0 hour for T in the above equation.

_{$$\begin{gathered} \mathrm{v}=\frac{800\mathrm{km}\left({\displaystyle \frac{{10}^3\mathrm{m}}{1\mathrm{km}}}\right)}{1.0\mathrm{hr}\left({\displaystyle \frac{3600\mathrm{s}}{1\mathrm{hr}}}\right)} \\ =222.2\mathrm{m}/\mathrm{s} \end{gathered}$$}

Convert the speed in m/s as,

_{$$\begin{gathered} \mathrm{v}=\left(222.2\mathrm{m}/\mathrm{s}\right)\left(\frac{1\mathrm{km}}{{10}^3\mathrm{m}}\right)\left(\frac{3600\mathrm{s}}{1\mathrm{hr}}\right) \\ =799.9\mathrm{km}/\mathrm{hr} \end{gathered}$$}

Hence, the speed of sound wave in m/s is 222.2 m/s and in km/hr is 799.9 km/hr