A cello string vibrates in its fundamental mode with a frequency of 335 1/s. The vibrating segment is 28.5 cm long and has a mass of 1.47 g. Find the tension in the string.

Tension on the string is 188.14N

Explanation:

Using V^2 = T / (m/l)

Where V = velocity

T = tension

m/l = density

Wavelength made for an open tube = 2L

Where L = length of string

Velocity = frequency * wavelength

Wavelength = 2 * 0.285m = 0.57m

Velocity = 335*0.57 = 190.95m/s

Density=m/l = 0.00147/0.285 = 0.00516kg/m

V^2 = T / (m/l)

190.95 = T / 0.00516

T = 190.95 * 0.00516 = 188.14N

The tension in string is found to be 188.06 N

Explanation:

For the vibrating string the fundamental frequency is given as:

f1 = v/2L

where,

f1 = fundamental frequency = 335 Hz

v = speed of wave

L = length of string = 28.5 cm = 0.285 m

Therefore,

v = f1 2L

v = (335 Hz) (2) (0.285)

v = 190.95 m/s

Now, for the tension:

v = √T/μ

v² = T/μ

T = v² μ

where,

T = Tension

v = speed = 190.95 m/s

μ = linear mass density of string = mass/L = 0.00147 kg/0.285 m = 5.15 x 10^-3 kg/m

Therefore,

T = (190.95 m/s) ² (5.15 x 10^-3 kg/m)

T = 188.06 N