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

Answer:

The correct solution is "1.2 m".

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,

⇒  $V=f\times \lambda$

or,

⇒  $f=\frac{V}{\lambda}$

On substituting the values, we get

⇒      $=\frac{2}{1.5}$

⇒      $=1.33 \ Hz$

hence,

⇒  $\lambda_1=\frac{V_1}{f}$

On substituting the values, we get

⇒       $=\frac{1.6}{1.33}$

⇒       $=1.2 \ m$