Vibrations with frequency 6.00 × 10² Hz are established on a 1.33-m length of string that is clamped at both ends.The speed of waves on the string is 4.00 × 10² m/s.
-How many antinodes are observed for the resulting standing wave pattern?
A)2
B)3
C)4
D)5
E)6

Question

Quizplus · Accepted Answer

For a standing wave with a frequency of 6.00 × 10² Hz, the wavelength is given by λ = v/f = (4.00 × 10² m/s)/(6.00 × 10² Hz) = 0.667 m. 
The length of the string is 1.33 m, which is exactly 2 times the wavelength. This means that there will be 2 antinodes in the standing wave pattern. However, we need to count the nodes as well. 
At the ends of the string, there will be nodes, since the string is clamped there and cannot move. Therefore, there will be 2 additional nodes. 
So, in total, there will be 2 + 2 = 4 antinodes observed in the standing wave pattern. 
Hence, the best choice is C.

Vibrations with Frequency 6