A string has a linear density of 5.3 x 10-3 kg/m and is under a tension of 370 N. The string is 1.8 m long, is fixed at both ends, and is vibrating in the standing wave pattern shown in the drawing. Determine the (a) speed, (b) wavelength, and (c) frequency of the traveling waves that make up the standing wave.
(A)Mass per unit length mₒ=5.3•10^-3 kg/m
Velocity of the wave in the stretched string is
v = sqrt(T/mₒ)
(B)The wavelength can’t be determined without the drawing.
Usually the wavelength (of the travelling wave!) is the distance between the first and the third nods of the standing wave.
(C) λ=v/f
To determine the speed, wavelength, and frequency of the traveling waves that make up the standing wave, we can use the following formulas:
1. Speed (v) of a wave is given by the equation v = √(T/μ), where T is the tension and μ is the linear density.
2. Wavelength (λ) can be determined using the equation λ = 2L/n, where L is the length of the string and n is the number of nodes present in the standing wave pattern.
3. Frequency (f) is given by the equation f = v/λ, where v is the speed and λ is the wavelength.
Now let's calculate the values step by step:
Step 1: Calculate the speed (v):
v = √(T/μ)
v = √(370 N / 5.3 x 10-3 kg/m)
v = √(370 / 5.3 x 10-3) m/s
v ≈ 80.19 m/s (rounded to two decimal places)
Step 2: Calculate the wavelength (λ):
λ = 2L/n
λ = 2 * 1.8 m / 2
λ = 1.8 m
Step 3: Calculate the frequency (f):
f = v/λ
f = 80.19 m/s / 1.8 m
f ≈ 44.55 Hz (rounded to two decimal places)
Therefore, the answers are:
(a) The speed of the traveling waves is approximately 80.19 m/s.
(b) The wavelength of the traveling waves is 1.8 m.
(c) The frequency of the traveling waves is approximately 44.55 Hz.