A 24\" long steel guitar string (linear density = 4.8 x 10-3 kg/m3) is to be tun
ID: 1259854 • Letter: A
Question
A 24" long steel guitar string (linear density = 4.8 x 10-3 kg/m3) is to be tuned to 406 Hz.a) What must the tension be?
b) If the string is not in tune at 406 Hz, and one hears a beat frequency 2 Hz using a tuning fork, what are the possible frequencies the string is currently tuned to?
c) To play the the harmonic f2 of 406 Hz, at what distance from the bridge must the string be fingered?
d) What is the frequency of the sound wave when the tuned string is played at full length?
e) What is the wavelength of the sound wave striking the ear at 23 deg C from the tuned frequency at 406 Hz? A 24" long steel guitar string (linear density = 4.8 x 10-3 kg/m3) is to be tuned to 406 Hz.
a) What must the tension be?
b) If the string is not in tune at 406 Hz, and one hears a beat frequency 2 Hz using a tuning fork, what are the possible frequencies the string is currently tuned to?
c) To play the the harmonic f2 of 406 Hz, at what distance from the bridge must the string be fingered?
d) What is the frequency of the sound wave when the tuned string is played at full length?
e) What is the wavelength of the sound wave striking the ear at 23 deg C from the tuned frequency at 406 Hz?
Explanation / Answer
speed v = sqrt(T/u)
a) v = sqrt(T/u)
T = v^2*u = 6100*6100*4.8e-3 = 178608 N
b) f = 406+2 = 408 Hz or 409-2 = 404 Hz
c)
x = L/2 = 12"
d) f1 = f2/2 = 203 Hz
e) wavelength = 2x = 22"