A backyard pool is 14.3 m long. For fun Sally uses a board to create waves. Sall

Question

A backyard pool is 14.3 m long. For fun Sally uses a board to create waves. Sally investigates the effect these waves have on Susan who is floating on another board near the middle of the pool. Sally notices that the waves travel with a speed 7.8 m/s. If Sally moves the board up and down (ie. through one complete oscillation) every 0.69 s what wavelength does Susan observe?

Wavelength = Answer m

Sally notices that when she moves the board at certain speeds standing waves are produced. When a standing wave is established does Susan (who remains above the same point on the bottom of the pool) move up and down?

Choose the best answer.

Select one:

1- No, as it is a standing wave Susan is stationary.

2- Yes, Susan will move up and down.

3-Maybe, it depends on exactly where Susan is in the pool.

Sally sets up a standing wave with two peaks and two troughs (these alternate with time, so the peak becomes a trough and then a peak again) along the length of the pool (there is no movement at the two ends of the pool). The wave speed remains the same, what period is Sally moving the board with now?

T = Answer s

To investigate this a little further Sally ties a mass to the end of a rope with a linear density of 10.0g/m (grams per meter) and runs the rope above the ground along the length of the pool. She hangs the end of the rope with the mass attached over a bit of fencing at the end of the pool. The weight of the mass creates tension in the rope. Sally now sets up a standing wave in this rope with the same number of crests as the wave in the pool (the ends of the rope, aligned with the ends of the pool, do not move). Sally finds that she needs to apply a frequency of 7.0 Hz to get the rope to move in this way.

What mass is hung from the end of the rope?

M=Answer kg

Explanation / Answer

(a) wavelength = velocity / frequency = velocity * period
= 7.8m/s * 0.69s = 5.38 m

(b) Maybe, it depends on exactly where Susan is in the pool.
If she is at a node, she is stationary; otherwise she moves up and down.

(c) With "two peaks and two troughs" and "no movements at the two ends," we have two complete waves in the pool, so the wavelength is
= L / 2 = 14.3m / 2 = 7.15 m.
Then period T = / v = 7.15m / 7.8m/s = 0.916 s


(d) Like the waves in the water, the rope has wavelength = 7.15 m
We're given the frequency, so we can find the velocity:
v = f = 7.15m * 7Hz = 50.05 m/s
Now we can use v = (T / µ)
T = µv² = 0.0100kg/m * (50.05m/s)² = 25.05 N
which means the mass is
m = T / g = 25.05N / 9.8m/s² = 2.55 kg

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