Avery long string (linear density 0.7 kg/m ) is stretched with a tension of 70 n . one end of the string oscillates up and down with an amplitude of 7 cm and a period of 0.35 s . what is the wavelength of the waves created in the string?

To develop this problem it is necessary to apply the concepts related to Wavelength, The relationship between speed, voltage and linear density as well as frequency. By definition the speed as a function of the tension and the linear density is given by

Where,

T = Tension

Linear density

Our data are given by

Tension , T = 70 N

Linear density ,

Amplitude , A = 7 cm = 0.07 m

Period , t = 0.35 s

Replacing our values,

Speed can also be expressed as

Re-arrange to find \lambda

Where,

f = Frequency,

Which is also described in function of the Period as,

Therefore replacing to find

Therefore the wavelength of the waves created in the string is 3.49m

need to see circuit to get time constant

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s