A wire of length 400cm is stretched between two fixed points. When plucked, its fundamental frequency is 150Hz. Calculate the speed of the wave produced.

Answer Details

The speed of a wave can be calculated using the formula: v = fλ where v is the wave speed, f is the frequency of the wave, and λ is the wavelength of the wave. In this problem, we are given the length of the wire, but we need to find the wavelength of the wave. The fundamental frequency of a stretched wire fixed at both ends is given by: f = (1/2L) * √(T/μ) where L is the length of the wire, T is the tension in the wire, and μ is the linear mass density of the wire. We are given the length of the wire (L) and the fundamental frequency (f), so we can solve for T/μ: T/μ = (2Lf)^2 Now we can use the wavelength formula to find the wave speed: v = fλ = f * 2L We know f and L, so we can plug in those values and solve for v: v = 150Hz * 2 * 400cm v = 120000cm/s We need to convert centimeters per second to meters per second: v = 1200m/s Therefore, the speed of the wave produced is 1200 m/s. The answer is option (C).