Answer

Verified

415.8k+ views

**Hint:**The distance two consecutive is equal to wavelength $\lambda $. Calculate the distance between 2$^{nd}$ crest and 6$^{th}$ trough in terms of the wavelength $\lambda $. Then use the formula $v=f\lambda $ to find the frequency of the boat.

**Formula used:**

$v=f\lambda $

**Complete step by step answer:**

In a wave, the maximum amplitude is called crest and the minimum amplitude is called trough. The distance between two consecutive crests or two consecutive troughs is equal to the wavelength ($\lambda $) of the wave.

At the middle of the distance between two consecutive crests lies a tough. The distance between the two crests is $\lambda $. Therefore, the distance between crest and its successive trough is $\dfrac{\lambda }{2}$.

Therefore, distance between the 2$^{nd}$ crest and 6$^{th}$ crest will be 4$\lambda $ and the distance between the 6$^{th}$ crest and the 6$^{th}$ will be $\lambda $. Hence, the total distance between the 2$^{nd}$ crest and 6$^{th}$ trough is $4\lambda +\dfrac{\lambda }{2}=\dfrac{9\lambda }{2}$.

And it is given that the distance between the 2$^{nd}$ crest and 6$^{th}$ trough is 24cm.

Therefore, $\dfrac{9\lambda }{2}=24cm$

$\Rightarrow \lambda =\dfrac{48}{9}=\dfrac{16}{3}cm=\dfrac{16}{3}\times {{10}^{-2}}m$.

Since, the boat is oscillating on the wave, the frequency of the boat will be equal to the frequency of the wave. Therefore, let us find the frequency of the wave. For this, we will use the formula $v=f\lambda $….(i), where f is the frequency and v is the speed of the wave.

It is given that the speed of the crest is 20$m{{s}^{-1}}$. Hence, the speed of the wave is 20$m{{s}^{-1}}$.

$\Rightarrow v=20m{{s}^{-1}}$

Substitute the values of $\lambda $ and v in equation (i).

$\Rightarrow 20=f\dfrac{16}{3}\times {{10}^{-2}}$

$\Rightarrow f=\dfrac{20\times 3\times {{10}^{2}}}{16}=\dfrac{1500}{4}=375Hz$

Therefore, the frequency of rocking of the boat is 375 Hz.

**Hence, the correct answer is option C.**

**Note:**

Sometimes, the question may ask to find the time period of oscillations. That time you may use the relation between time period and frequency of a wave. i.e. $T=\dfrac{1}{f}$.

We can also write the time period (T) in terms of wavelength since $f=\dfrac{v}{\lambda }$.

Therefore, $T=\dfrac{\lambda }{v}$.

Recently Updated Pages

Differentiate between Shortterm and Longterm adapt class 1 biology CBSE

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Define limiting molar conductivity Why does the conductivity class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Name 10 Living and Non living things class 9 biology CBSE

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE