One of the 64.3-cm-long strings of an ordinary guitar is tuned to produce the note LaTeX: B_3B 3 (frequency 245 Hz) when vibrating in its fundamental mode. The speed of sound in the surrounding air is 345 m/s. Find the speed of transverse waves on this string. Give an answer in m/s. Pay attention to the number of significant figures.

Question

Physics

Cohen Bowers

15 April, 21:48

One of the 64.3-cm-long strings of an ordinary guitar is tuned to produce the note LaTeX: B_3B 3 (frequency 245 Hz) when vibrating in its fundamental mode. The speed of sound in the surrounding air is 345 m/s. Find the speed of transverse waves on this string. Give an answer in m/s. Pay attention to the number of significant figures.

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Answers (1)

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Eliezer Weiss · Answer 1

v = 315 m/s

Explanation:

given,

length of the string = 64.3 cm

frequency at fundamental mode = 245 Hz

speed of sound = 345 m/s

speed of the transverse waves = ?

here

wavelength = twice length of string

λ = 2 L

λ = 2 * 64.3

λ = 128.6 cm = 1.286 m

using formula

v = ν λ

v = 245 * 1.286

v = 315.07 m/s

Hence, the speed of the transverse wave on the string will be equal to v = 315 m/s