A string has a linear density of 6.7 x 10-3 kg/m and is under a tension of 210 N. The string is 1.6 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.
In the diagram, there are 2 nodes and 3 half wave cycles. I only need help with b and c.
The distance between nodes is 1/2 wavelength.
if you have speed, frequency(wavelength)=speed
To determine the wavelength (b) and frequency (c) of the traveling waves that make up the standing wave, we can use the given information and equations related to wave speed.
The wave speed (v) can be calculated using the following equation:
v = √(T/μ)
where T is the tension in the string and μ is the linear density of the string.
Substituting the given values:
T = 210 N
μ = 6.7 x 10^-3 kg/m
v = √(210 / 6.7 x 10^-3)
Calculating the wave speed v will give us the answer to part (a), which is not included in this question.
To find the wavelength (λ) of the standing wave, we can use the relationship:
λ = 2L/n
where L is the length of the string and n is the number of antinodes in the standing wave.
Given:
L = 1.6 m
n = 3 (since there are 3 half-wave cycles, there will be 3 antinodes.)
Substituting the values:
λ = 2 x 1.6 / 3
To find the frequency (f) of the standing wave, we can use the equation:
f = v / λ
Now, we can substitute the calculated values of v and λ to find f.
f = v / λ
Finally, we can calculate the wavelength (b) and frequency (c) of the traveling waves that make up the standing wave using the formulas above.