Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . Determine the wave speed, the wavelength and the frequency of the wave.
Options
- A10 m s ⁻¹ , 10 cm , 100 Hz
- B5 m s ⁻¹ , 40 cm , 25 Hz
- C20 m s ⁻¹ , 20 cm , 50 Hz
- D10 m s ⁻¹ , 20 cm , 50 Hz
Correct answer
D. 10 m s ⁻¹ , 20 cm , 50 Hz
Step-by-step solution
Comparing the given wave equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] with the standard wave equation y = A (kx + t) , we get: k = 31.4 m ⁻¹ and = 314 s ⁻¹ The wave speed is given by v = k v = 314 31.4 = 10 m s ⁻¹ The wavelength is given by = 2 k = 2 3.14 31.4 = 0.2 m = 20 cm The frequency is given by f = 2 f = 314 2 3.14 = 50 Hz Thus, the wave speed is 10 m s ⁻¹ , wavelength is 20 cm and frequency is 50 Hz .