# Speed of Ripples in a Pond

1. Mar 23, 2014

### leeone

Do the speed of the ripples, or waves, in a pond depend on the weight of the pebble thrown into the water? I would think the answer is no since it should only depend on the properties of the water. Similarly if you take a rope and jerk it violently (more force) compared to softly (less force) and the rope has a fixed tension...the wave would have the same speed in both cases, no?

2. Mar 23, 2014

### euquila

When you toss a stone into the pond you then see a wave "packet" that moves out with speed v_pack. This wave packet is as per the attached image. The peaks of the waves inside the wave packet all move with the same speed that is twice as fast as the packet itself v_waves = 2 * v_pack. Notice how the waves inside the packet are small at the ends of the packet and large in the middle. This explains why, when sitting on the dock of a lake and a boat goes by, the noise of the waves hitting the dock start soft build up loudly and then goes soft again.

Dropping a bigger stone into the water will only make the amplitudes of the waves larger. However, because water is a dispersive medium (due to the viscosity and imperfections of the water) the speed of the wave will depend on its frequency and will slow down a bit as the envelope stretches (like someone pulling it apart at both end).

Ya waves are very hard to pin down and, although look quite graceful, the mathematics can be tough.

#### Attached Files:

• ###### wave_packet.gif
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3. Mar 24, 2014

### leeone

Okay that answers my question. Thank you.