The fourth harmonic of the lowest string on a guitar has a frequency f4 = 330 Hz

Question

The fourth harmonic of the lowest string on a guitar has a frequency f4 = 330 Hz. The speed of waves on the string is 99.0 m/s.

(a) What is the wavelength of the waves on the string?

(b) What is the wavelength of the sound waves radiated into the air by the string? Assume the speed of sound in air is 343 m/s.

(c) When the string sounds, the sound power radiated by the guitar is 1.13 mW. Assuming the sound is radiated equally in all directions, find the intensity of the sound 3.0 m away from the instrument.

(d) At what distance from the guitar will the intensity be one fourth your answer to part (c)?

Explanation / Answer

Part A)

v = f(wavelength)

99 = 330(wavelength)

wavelength = .30 m (30 cm)

Part B)

343 = 330(wavelength)

wavelength = 1.04 m

Part C)
I = P/A

I = (1.13 X 10^-3)/(4pi)(3^2)

I = 9.99 X 10^-6 W/m^2

Part D)

9.99 X 10^-6/4 = 2.50 X 10^-6

2.50 X 10^-6 = (1.13 X 10^-3)/(4pi)r^2

r = 6 m

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