Question

You have two vibrating objects in an infinitely large pool. The distance between them is 5.8 m . Their frequency of vibration is 2.0 Hz and the wave speed is 3.3 m/s . The vibrations are sinusoidal.

Find a location between them where the water does not vibrate. Assume n=0 .

Find another location between them where the water vibrates with the largest amplitude. Assume n=0 .

Answer 1

Wave length of the vibrating waves is the of ratio of wave velocity and frequency. Lambda = v/y = 3.3 m/s/2.0 Hz = 1.65 m Number of waves between 0 to 5.8 m is, n = 5.8 m/1.65 m = 3.5 At node (minimum amplitude) water does not vibrate, let l = lambda/4 = 1.65m/4 almostequalto 0.4 m At Anti - node (maximum amplitude) water vibrate largest amplitude, let l = lambda/2 = 1.65 m/2 almostequalto 0.8m Condition l lessthanorequalto 5.8 (nodes and anti nodes are produced) Example: Next node at l = 3 lambda/4 = 3 (0.4m) = 1.2 m Nest anti node at l = lambda/2 + lambda/2 = (0.8) = 1.6 m and so on