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(1) A guitar string of length L = 60 cm and mass 1.2 g is tuned to produce the n

ID: 1837012 • Letter: #

Question

(1) A guitar string of length L = 60 cm and mass 1.2 g is tuned to produce the note B3 (frequency f1 = 245 Hz) when vibrating in its fundamental mode (a) Find the string tension and the speed of transverse waves on this string. (b) If the tension is increased by 5%, what will be the new fundamental Irequency of the string! (c) If the speed of sound in air is 345 m/s, find the frequency and wavelength of the sound wave produced in the air by the vibration of the B3 string (in its original tension)

Explanation / Answer

1) wavelength = 2L= 1.2m

so speed = freq*wavelength = 1.2*245=295m/s

and

speed = sqrt(TL/m)

this gives T=speed^2*m/L=295^2*0.0012/0.6=174.05N

b) if tension is increases by 5percent then speed increases by 2.5 percent andn so frequency increases by 2.5 percent.

so new fundamental freq = 245*1.025=251.125Hz

c)the frequency is that of the string = 245Hz

wavelength = speed / frequency = 345/245=1.408m

d)