The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by y = (0 4 cm) sin[(0.314 cm − 1 )x] cos[(600 π s − 1 )t] (A) What is the frequency of vibration? (B) What are the positions of the nodes? (C) What is the length of the string? (D) What is the wavelength and the speed of two travelling waves that can interface to give this vibration?

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by
y = (04 cm) sin[(0.314 cm⁻¹)x] cos[(600π s⁻¹)t]

(A) What is the frequency of vibration? (B) What are the positions of the nodes? (C) What is the length of the string? (D) What is the wavelength and the speed of two travelling waves that can interface to give this vibration?

We can write the stationary wave equation as,

From this we can say,

So, f=300 Hz (A)

So, nodes are at 10 cm, 20 cm, 30 cm. (B)

The length of the string can be determined as,

(C)

The wave equation is,

From this we can get,

So,

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