Question

13. A large stone is dropped in a still pond generating water waves. The amplitude of a generated wave is 15 cm at a distance 9 cm from the center where the stone is dropped. Then the amplitude of the wave at 100 cm from the center is
A. 6.75 cm B. 9.0 cm C. 2.25 cm D. 4.5 cm​

Answer 1

Explanation:

Let's assume that the ripple was created in a pool of water at the center so that with time the ripple moves away.

Let the energy of the ripple be E .

At a distance of 5 cm from the point of origin the amplitude is 4 cm.

Energy distributed in circle of circumference 2π5 cm.

Energy per unit length, E

1

=

10π

E

When it reaches 10 cm, E

2

=

2π×10

E

=

2

E

1

Now energy is proportional to square of amplitude (A).

Thus if per unit energy decreases by

2

1

, then amplitude will decrease by

2

1

.

New amplitude, A

1

=

2

4

=

8