Question

A stretched string has a mass per unit length of 5.40 g/cm and a tension of 17.5 N. A sinusoidal wave on this string has an amplitude of 0.157 mm and a frequency of 92.2 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x,t) = ym sin(kx + ωt), what are (a) ym, (b) k, and (c) ω, and (d) the correct choice of sign in front of ω?

Answer 1

Part a)

`y_m = 0.157 mm`

part b)

`k = 101.8 rad/m`

Part c)

`\omega = 579.3 rad/s`

Part d)

here since wave is moving in negative direction so the sign of
`\omega` must be positive

Step-by-step explanation:

As we know that the speed of wave in string is given by

`v = \sqrt{(T)/(m/L)}`

so we have

`T = 17.5 N`

`m/L = 5.4 g/cm = 0.54 kg/m`

now we have

`v = \sqrt{(17.5)/(0.54)}`

`v = 5.69 m/s`

now we have

Part a)

`y_m` = amplitude of wave

`y_m = 0.157 mm`

part b)

`k = (\omega)/(v)`

here we know that

`\omega = 2\pi f`

`\omega = 2\pi(92.2) = 579.3 rad/s`

so we have

`k = (579.3)/(5.69)`

`k = 101.8 rad/m`

Part c)

`\omega = 579.3 rad/s`

Part d)

here since wave is moving in negative direction so the sign of
`\omega` must be positive