The wavelength of waves produced on the surface of water is 20 cm. If the wave velocity is 24 ms^-1, calculate (i) the number of waves produced in one second and (ii) the time in which one wave is produced.

(i) As we know,

Velocity (V) = frequency (f) x wavelength (λ)

Given,

V = 24 ms^-1

λ = 20 cm

Converting cm to m, we get,

100 cm = 1 m,

1 cm = $\dfrac{1}{100}$ m = 0.01 m,

Therefore, 20 cm = (20 x 0.01) m = 0.2 m

Hence, λ = 0.2 m

Substituting the values in the formula above, we get,

$24 = f \times 0.2 \\[0.5em] \Rightarrow f = \dfrac{24}{0.2} \\[0.5em] \Rightarrow f = \dfrac{240}{2} \\[0.5em] \Rightarrow f = 120 s ^{-1}\\[0.5em]$

Therefore, the number of waves produced in one second = 120 s^-1

(ii) As we know,

Time in which one wave is produced (t) = $\dfrac{1}{f}$

Substituting the values in the formula above, we get,

$t = \dfrac{1}{120} \\[0.5em] \Rightarrow t = 0.0083 \\[0.5em] \Rightarrow t = 0.0083 s \\[0.5em]$

Hence,

Time in which one wave is produced = 8.3 x 10^-3 s