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.
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).