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A string of length L = 2.2 m and mass m = 0.035 kg is fixed between two stationary points, and when the string is played a transverse wave of frequency f = 94 Hz is generated. The wave is vibrating in an unknown harmonic.

a. If the wavelength is 10.0 cm, which harmonic is this, counting the fundamental as 1?
b. For the case described in Part (a), what is the tension in N?

User Parze
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Final answer:

The transverse wave with a wavelength of 10.0 cm on a string with a length of 2.2 m corresponds to the 22nd harmonic. The tension in the string is approximately 688.64 N.

Step-by-step explanation:

To determine the harmonic of a transverse wave on a string with a given wavelength, we can use the formula:

n = L / λ

Where n is the harmonic number, L is the length of the string, and λ is the wavelength of the wave.

In this case, the length of the string is 2.2 m and the wavelength is 10.0 cm (0.1 m).

Plugging these values into the formula, we get:

n = 2.2 m / 0.1 m = 22

Therefore, the transverse wave of frequency 94 Hz with a wavelength of 10.0 cm corresponds to the 22nd harmonic.

b. To find the tension in the string, we can use the formula:

T = (μ × (2L × f)^2) / 4L

Where T is the tension in the string, μ is the mass per unit length of the string, L is the length of the string, and f is the frequency of the wave.

In this case, the mass of the string is 0.035 kg, the length is 2.2 m, and the frequency is 94 Hz.

Plugging these values into the formula, we get:

T = (0.035 kg/m × (2 × 2.2 m × 94 Hz)^2) / (4 × 2.2 m) = 688.64 N

Therefore, the tension in the string is approximately 688.64 N.

User Andbeonetraveler
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