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The speed of surface waves in water decreases as the water becomes shallower
The speed of surface waves in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake with a speed of 2.2 m/s and a wavelength of 1.35 m. When these waves move into a shallower part of the lake, their speed decreases to 1.6 m/s, though the frequency remains the same. Find the wavelength of the waves in the shallower water.
Expert Solution
The complete solution is as shown below.
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Step-by-step explanation
Given:
?v1?=2.2m/sλ1?=1.35mv2?=1.6m/sλ2?=???
The relationship between wavelength, frequency and velocity is given as,
?v=fλ?
So, for both conditions the equation is given as,
?v2?v1??=fλ2?fλ1??1.62.2?=λ2?1.35?λ2?=0.981m??
Answer: The wavelength of the waves in the shallower water is 0.981 m.
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