Question

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.

Answer 1

Tension on the string is 188.14N

Step-by-step 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

Answer 2

The tension in string is found to be 188.06 N

Step-by-step 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