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.

We can't see your drawing. The number of half-waves must be known.

in the drawing there are three half waves and 2 nodes

To determine the speed, wavelength, and frequency of the traveling waves that make up the standing wave, we can use the following formulas:

(a) Speed (v) = Frequency (f) * Wavelength (λ)
(b) Wavelength (λ) = 2 * Length (L) / n (where n is the number of nodes in the wave)
(c) Frequency (f) = Speed (v) / Wavelength (λ)

Given:
Linear density (μ) = 6.7 x 10^(-3) kg/m
Tension (T) = 210 N
Length (L) = 1.6 m

Let's start by finding the speed of the wave.

Step 1: Calculate the mass of the string.
Mass (m) = Linear Density (μ) * Length (L)
m = (6.7 x 10^(-3) kg/m) * 1.6 m
m = 0.01072 kg

Step 2: Calculate the speed of the wave.
Speed (v) = √(Tension (T) / Linear Density (μ))
v = √(210 N / 0.01072 kg)
v = √19612.68 m^2/s
v = 140 m/s

The speed of the traveling waves that make up the standing wave is 140 m/s.

Next, let's find the wavelength.

Step 3: Determine the number of nodes (n).
From the given drawing, we can see that there are two nodes. Therefore, n = 2.

Step 4: Calculate the wavelength.
Wavelength (λ) = 2 * Length (L) / n
λ = 2 * 1.6 m / 2
λ = 1.6 m

The wavelength of the traveling waves that make up the standing wave is 1.6 m.

Finally, let's find the frequency of the wave.

Step 5: Calculate the frequency.
Frequency (f) = Speed (v) / Wavelength (λ)
f = 140 m/s / 1.6 m
f = 87.5 Hz

The frequency of the traveling waves that make up the standing wave is 87.5 Hz.

To summarize:
(a) The speed of the traveling waves is 140 m/s.
(b) The wavelength of the traveling waves is 1.6 m.
(c) The frequency of the traveling waves is 87.5 Hz.