A string has a linear density of 6.2 x 10-3 kg/m and is under a tension of 250 N. The string is 1.2 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.

Isn't there a standard formula for this?

To determine the speed, wavelength, and frequency of the traveling waves that make up the standing wave, we can use the relationship between these quantities.

(a) Speed:
The speed of a wave can be found using the equation v = √(T/μ), where v is the speed of the wave, T is the tension in the string, and μ is the linear density of the string.

Given: T = 250 N and μ = 6.2 x 10^(-3) kg/m.
Substituting these values into the equation, we can calculate the speed of the wave.

v = √(250 N / 6.2 x 10^(-3) kg/m)
= √(4.032 x 10^4 m^2/s^2)
≈ 200.8 m/s

Therefore, the speed of the wave is approximately 200.8 m/s.

(b) Wavelength:
The wavelength of a wave can be determined by dividing the speed of the wave (v) by the frequency (f). Mathematically, it can be expressed as: λ = v/f, where λ represents wavelength.

Given: v = 200.8 m/s
To calculate the wavelength, we need to determine the frequency.

(c) Frequency:
In a standing wave pattern, the frequency can be found using the equation f = n * v/2L, where n represents the number of nodes, v is the speed of the wave, and L is the length of the string.

Given: v = 200.8 m/s and L = 1.2 m.
From the image, we can observe that there is one complete wavelength between the fixed ends of the string. This implies that there is one node present in the standing wave pattern.

Substituting these values into the equation, we can determine the frequency.

f = 1 * (200.8 m/s) / (2 * 1.2 m)
= 83.7 Hz

Therefore, the frequency of the wave is 83.7 Hz.

Now we can use the frequency (f) obtained to calculate the wavelength (λ).

λ = v/f
= (200.8 m/s) / (83.7 Hz)
≈ 2.4 m

Hence, the wavelength of the wave is approximately 2.4 m.

In summary,
(a) The speed of the wave is approximately 200.8 m/s.
(b) The wavelength of the wave is approximately 2.4 m.
(c) The frequency of the wave is 83.7 Hz.