Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
A string, 2 m long and fixed at both ends, is set into vibrations in its first overtone. The wave speed on the string is 200 m s ⁻¹ and the amplitude is 0.5 cm . Determine the wavelength and the frequency.
Options
- A2 m , 100 Hz
- B4 m , 50 Hz
- C1 m , 200 Hz
- D4 3 m , 150 Hz
Correct answer
A. 2 m , 100 Hz
Step-by-step solution
For a string of length L fixed at both ends, the wavelength of the n -th harmonic is given by = 2L n . The first overtone corresponds to the second harmonic, so n = 2 . Substituting L = 2 m and n = 2 : = 2 2 2 = 2 m The frequency of the wave is given by f = v . Given the wave speed v = 200 m s ⁻¹ : f = 200 2 = 100 Hz