Question

A seismic wave travels from rock into sea water. In rock, the wave has a speed of 3,950 m/s and a wavelength of 560m. In seawater, the wave has a speed of 1,500 m/s.

Calculate the wavelength of the seismic wave in seawater.
Write your answer to the nearest tenth.

Answer 1

This question involves the concepts of wave speed, wavelength, and frequency.

The frequency of the wave in seawater will be "2.68 Hz".

FREQUENCY

The relationship between speed, wavelength, and frequency of the wave can be given by the following formula:

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

Here, the wavelength of the wave is a constant property. Therefore,

$\frac{v_1}{f_1}=\frac{v_2}{f_2}$

where,

• v₁ = speed of the wave in the rock = 3950 m/s
• v₂ = speed of the wave in the seawater = 1500 m/s
• λ = wavelength = 560 m
• f₁ = frequency of the wave in the rock = $f_1=\frac{v_1}{\lambda}=\frac{3950\ m/s}{560\ m} = 7.05\ Hz$
• f₂ = frequency of the wave in the seawaater = ?

Therefore,

$\frac{3950\ m/s}{7.05\ Hz}=\frac{1500\ m/s}{f_2}\\\\f_2=\frac{(1500\ m/s)(7.05\ Hz)}{3950\ m/s}$

f₂ = 2.68 Hz

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