Just as you are about to step into a nice hot bath, a small earthquake rattles y

Question

Just as you are about to step into a nice hot bath, a small earthquake rattles your bathroom. Immediately afterward, you notice that the water in the tub is oscillating. The water in the center seems to be motionless while the water at the two ends alternately rises and falls, like a seesaw. There are no other points where the water seems to be motionless. You happen to know that your bathtub is 1.3m long, and you count 10 complete oscillations of the water in 20s .

1.What is the wavelength of this standing wave?

Explanation / Answer

the bathtub has a length = 1.3 m and it contains one end with crest and other with a trough.

thus the wavelength must be 2*1.3 = 2.6 m casue only if it had been twice long the other crest would have arisen and thus the wavelength.

velocity = wavelength * frequency..... here freq.= 10/20 = 0.5

thus v= 2.6 * 0.5 = 1.3m/s

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