A guitar string is plucked and sound waves are produced 1 If

A guitar string is plucked and sound waves are produced.

1.) If the string tension, FT, is decreased four-fold, the fundamental frequency,f1, will be ________ the original frequency.

2.) If a second string of half length,L, and same mass,m, is played, the fundamental frequency,f1, of the second string will be _______ the frequency of the other string.

3.) The sound wave wavelength, is _______ the string wavelength.

4.)If the finger and fret is moved to the 1/4 the length on the guitar string, the frequency will be ______ the original frequency.

5.) The wavelength,on the string for the 3^th harmonic of the frequency is ______ the wavelength of the fundamental frequency

6.)The wavelength,of the sound wave is ______ the wavelength of the wave on the guitar string.

Solution

1) v = sqrt[ FT / linear mass density ]

and f = v / wavelength

hence f is directly propotional to sqrt(FT).

so frequency will 2 -fold (double) of origial frequency.

(2) linear density = m / L

now mass is same and L is halved. hence linear density is doubled.

and wavelength willalso change.

new wavelength will be half of initial.

so new frequency will be 2/sqrt(2) OR 1.414 times of original frequency.

(3) both will be equal.

(4) new wavelength = 1/4 times of original.

and f = v / wavelength

so new frequency will be 4 times of original one.

(5) for 3rd hormonic, frequency is 3 times.

hence wavelength will be 1/3 times of original one.

(6) same