Question Detail
Question
A 450 Hz tuning fork sets a string between two supports into vibration, producing one loop (the fundamental mode). If the amplitude of the vibration is 0.5 mm and the wave speed on the string is 250 m/s, what is the length of the string?
Correct Answer
Option B is the correct answer.
Detailed Explanation
For a string fixed at both ends, producing 'one loop' means it is vibrating in its fundamental mode (n=1). In this mode, the length of the string L is half a wavelength (L = λ/2).First, calculate the wavelength λ using the wave speed (v) and frequency (f): λ = v/f.λ = 250 m/s / 450 Hz = 5/9 m.Now, calculate the length of the string: L = λ/2 = (5/9 m) / 2 = 5/18 m.5/18 m ≈ 0.278 m.
Hint
Relate the number of loops to the wavelength and string length for a string fixed at both ends. Then, use the wave speed and frequency to find the wavelength.