A `6.00m` segment of a long string has a mass of `180 g`. A high-speed photograph shows that the segment contlains four complete cycles of a wave. The string is vibrating sinusoidally with a frequency of `50.0 Hz` and a peak - to - valley dispalcement of `15.0 cm`. (The "peak-to-valley" displacment is the vertical distance from the furthest positive displacement to the farther negative displacement.) (a) Write the funcation that describe this wave traveling in the positive `x` direction. (b) Determine the average power being supplied to the string.

A `6.00m` segment of a long string has a mass of `180 g`. A high-speed

1.	A `6.00m` segment of a long string has a mass of `180 g`. A high-speed photograph shows that the segment contlains four complete cycles of a wave. The string is vibrating sinusoidally with a frequency of `50.0 Hz` and a peak - to - valley dispalcement of `15.0 cm`. (The "peak-to-valley" displacment is the vertical distance from the furthest positive displacement to the farther negative displacement.) (a) Write the funcation that describe this wave traveling in the positive `x` direction. (b) Determine the average power being supplied to the string.
Answer» Correct Answer - (a) `y = (7.50 cm) sin ((4pi)/(3) xx -314t + phi)` (b) `(2025pi^(2))/(32) = 625 W` (a) `f = 500Hz` `mu = (180 xx 10^(-3))/(6) = 3 xx 10^(-2)Kg//m` `2A = 15 xx 10^(-2)m` `A = 7.5 xx 10^(-2)m` `4lambda = 6 , lambda = 3//2 m`. and `v = flambda = 75 m//sec` `omega = 2pif = 100pi` also `K = (omega)/(v) = (4pi)/(3)` If phase constant is `phi` then `:.` equation is `y = 7.5 xx 10^(-2) sin [100pit-(4pi)/(3)x + phi]` (b) `P_(av) = 2pi^(2)f^(2)A^(2)muv = (2025)/(32) pi^(2) = 625 w`

Discussion

No Comment Found

Related InterviewSolutions

A man generates a symmetrical pulse in a string by moving his hand up and down. At `t=0` the point in his hand moves downward. The pulse travels with speed of `3 m//s` on the string & his hands passes `6` times in each second from the mean position. Then the point on the string at a distance `3m` will reach its upper extreme first time at time `t=`
The equation `y=A cos^(2) (2pi nt -2 pi (x)/(lambda))` represents a wave withA. Amplitude `A//2` , frequency 2n and wavelength `lambda//2`B. Amplitude `A//2` , frequency 2n and wavelength `lambda`C. Amplitude A , frequency 2n and wavelength `2lambda`D. Amplitude A , frequency n and waves
A long string having a cross- sectional area `0.80 mm^2` and density `12.5 g cm^(-3)` is subjected to a tension of 64 N along the X-axis. One end of this string is attached to a vibrator moving in transverse direction at a frequency fo 20Hz. At t = 0. the source is at a maximujm displacement y= 1.0 cm. (a) Write the equation for the wave. (c ) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05 s ? (d) What is the velocity of this particle at this instant ?A. `10sqrt(2)pi cm//s`B. `40sqrt(2) pi cm//s`C. `30sqrt(2)pi cm//s`D. `20sqrt(2) pi cm//s`
A `6.00m` segment of a long string has a mass of `180 g`. A high-speed photograph shows that the segment contlains four complete cycles of a wave. The string is vibrating sinusoidally with a frequency of `50.0 Hz` and a peak - to - valley dispalcement of `15.0 cm`. (The "peak-to-valley" displacment is the vertical distance from the furthest positive displacement to the farther negative displacement.) (a) Write the funcation that describe this wave traveling in the positive `x` direction. (b) Determine the average power being supplied to the string.
A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that moves the end up and down through a distance by `2.0 cm`. the motion of bar is continuous and is repeated regularly `125` times per second. If klthe distance between adjacent wave crests is observed to be `15.6 cm` and the wave is moving along positive `x-`direction, and at `t=0` the element of the string at `x=0` is at mean position `y =0` and is moving downward, the equation of the wave is best described byA. `y=(1 cm) sin [(40.3 rad//m) x-(786 rad//s)t]`B. `y=(2 cm) sin [(40.3 rad//m) x-(786 rad//s)t]`C. `y=(1 cm) cos [(40.3 rad//m) x-(786 rad//s)t]`D. `y=(2 cm) cos[(40.3 rad//m) x-(786 rad//s)t]`
Find speed of the wave generated in the spring as in the sitution shown. Assume that the tension is not affected by the mass of the cord.
A metallic wire with tension `T` and at temperature `30^(@)C` vibrates with its fundamental frequency of `1 kHz`. The same wire with the same tension but at `10^(@)C` temperature vibrates with a fundamental frequency of `1.001 kHz`. The coefficient of linear expansion of the wire is equal to `10^(-K) .^(@)C`. Find `2K`.
The average power transmitted through a given point on a string supporting a sine wave is 0.20 W when the amplitude of the wave is 2.0 mm. What power will be transmitted through this point if the amplitude is increased to 3.0 mm.A. `0.40` wattB. `0.80` wattC. `1.2` wattD. `1.6` watt
A particle on a stretched string supporting a travelling wave, takess `5.0 ms` to move from its mean position to the extreme position. The distance between two consecutive particle, which are at their mean position, is `3.0 cm`. Find the wave speed `(in m//s)`.
shows the position of a medium particle at t=0, supporting a simple harmonic wave travelling either along or opposite to the positive x-axis. (a) write down the equation of the curve. (b) find the angle `theta` made by the tangent at point P with the x-axis. (c ) If the particle at P has a velocity `v_(p) m//s`, in the negative y-direction, as shown in figure, then determine the speed and direction of the wave. (d) find the frequency of the wave. (e) find the displacement equation of the particle at the origin as a function of time. (f) find the displacement equation of the wave.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment