Question

The speed of surface waves in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake withn a speed of 2m/s and a wavelength of 1.5m. When these waves move into a shallower part of the lake, their speed decreases to 1.6m/s, though their frequency remains the same. Find the wavelength of the wave in the shallower water.

Answer 1

The correct solution is "1.2 m".

Step-by-step explanation:

The given values are:

Wavelength of waves,

λ = 1.5 m

Speed of waves on surface,

V = 2 m/sec

Speed of waves in water,

V₁ = 1.6 m/sec

As we know,

⇒
`V=f* \lambda`

or,

⇒
`f=(V)/(\lambda)`

On substituting the values, we get

⇒
`=(2)/(1.5)`

⇒
`=1.33 \ Hz`

hence,

⇒
`\lambda_1=(V_1)/(f)`

On substituting the values, we get

⇒
`=(1.6)/(1.33)`

⇒
`=1.2 \ m`