A steel wire with mass 29.9 g and length 1.52 m is strung on a bass so that the

Question

A steel wire with mass 29.9 g and length 1.52 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m.

(a) Compute the linear density of the string.
kg/m

(b) What velocity wave on the string will produce the desired fundamental frequency of the E1 string, 41.2 Hz?
m/s

(c) Calculate the tension required to obtain the proper frequency.
N

(d) Calculate the wavelength of the string's vibration.
m

(e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is 343 m/s.)
m

Explanation / Answer

Given,

m = 29.9 g ; L = 1.52 m

a)We know that,

u = m/L = 0.0299/1.52 = 0.0197 kg/m

Hence, u = 0.0197 kg/m

b)we know that fundamental frequency is:

f = v/2L => v = 2 f L

v = 2 x 41.2 x 1.1= 90.64 m/s

Hence, v = 90.64 m/s

c)We know that,

v = sqrt (T/u)

90.64 = sqrt (T/0.0197)

8215.6096 = T/0.0197

T = 161.85 N

d)v = f lambda

lambda = v/f = 90.64/41.2 = 2.2 m

Hence, lambda = 2.2 m

e)lambda(sound) = v(cound)/f = 343/41.2 = 8.32 m

Hence, lambda(air) = 8.32 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.