Question

A string is vibrating in its fifth overtone between two rigid supports 2.4 m apart. The distance between successive node and antinode is

• A. 0.2 m
• B. 0.6 m
• C. 0.8 m
• D. 0.1 m

Answer 1

The Correct Option is A

The distance between successive nodes or antinodes in a vibrating string can be determined using the formula: 
L = \(\frac {λ}{2}\)
In this case, the string is vibrating in its fifth overtone. The fifth overtone corresponds to the fifth harmonic, which means there are five complete wavelengths within the given distance between the supports. 
So, the wavelength of the wave is: 
λ = \(\frac {L}{5}\) = \(\frac {2.4 \ m}{5}\) = 0.48 m 
Now, to find the distance between successive nodes or antinodes: 
Distance = \(\frac {λ}{2}\)= \(\frac {0.48 \ m}{2}\) = 0.24 m 
Therefore, the correct option is (A) 0.2 m.