Answer to Question #110575 in Physics for Mariline Renol

Question

2. Two students want to use a 12 m long rope to create standing waves. They first measure the speed at which a single wave pulse moves from one end of the rope to another and find that it is 36 m/s.
a. Use this information to determine the fundamental frequency of the rope. (1 mark)
b. Suppose the students cut the rope in half. The speed of the wave on the rope only depends on the material from which the rope is made and its tension, so it will not change. What effect does the shorter rope have on the wavelength and frequency? Do an example calculation to support your answer. (2 marks)

Answer 1

a)

$$f=\frac{v}{\lambda}=\frac{36}{12}=3\ Hz$$

b) The wavelength decreases, frequency increases.

$$L'=0.5L\to \lambda'=0.5(12)=6\ m$$

$$f'=\frac{v}{\lambda'}=\frac{36}{6}=6\ Hz$$