The drawing shows two strings that have the same length and linear density. The left end of each string is attached to a wall, while the right end passes over a pulley and is connected to objects of different weights (WA and WB). Different standing waves are set up on each string, but their frequencies are the same. If WA = 48 N, what is WB?

WB = 12 N

Explanation:

Solution:

- The relationship between wavelength (λ) and velocity (v) is given as:

                                       v  ∝ λ

- Both wavelength and and velocity are proportional. For the case B, we see that wavelength λ is halved. From using the above relation we can also say that velocity (v) is also halved.

- The relationship between velocity (v) and tension force (T) in the string is given by:

                                      v^2 ∝ T  

- We saw that if wavelength (λ) is halved, velocity (v) is halved then from the above relationship we see that Tension force T is reduced 4 times.

- Since the tension force T in part A is:

                                      TA = m*g = WA = 48

- The Tension force in part B, TB is reduced 4 times as follows:

                                      TB = 0.25*m*g = WB = 12 N