Question

11) What frequency and period would be required for Sally and her cheerful, pleasant, hard-working partner to produce a standing wave with three nodes? Explain your reasoning by identifying your stepsNOTE: This is relevant to problem 10, but problem 10 is already finished and it’s correct

Answer 1

Sally and her partner want to produce a standing wave with three nodes.

Let us first sketch the wave to better understand the problem.

As you can see, three nodes correspond to one standing wave.

Now, let us find the wavelength

`\lambda=(4\; m)/(1\; wave)=4\; m`

So, the wavelength is 4 m

(note: 4m is the distance between the end of the string given in problem 10)

The frequency of the wave is

`f=(v)/(\lambda)=(10\; (m)/(s))/(4\; m)=2.5\; Hz`

So, the frequency of the wave is 2.5 Hz

(note: the speed 10 m/s was found in problem 10)

Finally, the period of the wave is

`T=(1)/(f)=(1)/(2.5\; Hz)=0.40\; s`

So, the period of the wave is 0.40 s