The equation of a wave is `y=(x,t)=0.05 sin [(pi)/(2)(10x-40t)-(pi)/(4)]m` find: (a) the wavelength, the frequency and the wave velocity (b) the participle velocity and acceleration at `x=0.5m`and `t = 0.05s`.

The equation of a wave is `y=(x,t)=0.05 sin [(pi)/(2)(10x-40t)-(pi)/(4

1.	The equation of a wave is `y=(x,t)=0.05 sin [(pi)/(2)(10x-40t)-(pi)/(4)]m` find: (a) the wavelength, the frequency and the wave velocity (b) the participle velocity and acceleration at `x=0.5m`and `t = 0.05s`.
Answer» (a) The equation may be rewritten as, `y(x,t) = 0.05 sin (5 pi x - 20 pi t - (pi)/(4))m` Comparing this with equation of plane progressive harmonic wave, `y(x,t)=A sin(kx-omegat+phi)` we have number `k = (2pi)/(lamda) = 5 pi rad//m :. Lamda = 0.4 m` The angular frequency is, `omega=2pif=20 pirad//s :. f =1 0 Hz` The wave velocity is, `v = f lamda = (omega)/(k) = 4 ms^(-1)` in -x direction (b) The particle velocity and acceleration are, `V_(p)=(dely)/(delt)=-(20pi)(0.05)cos((5pi)/(2)-pi-(pi)/(4))=2.22 m//s` `a_(p)=(del^(2)y)/(delt^(2))==(20pi)^(2)(0.05)sin((5pi)/(2)-pi-(pi)/(4))=140 m//s^(2)`

Discussion

No Comment Found

Related InterviewSolutions

A sinusoidal voltage of amplitude 25 volts and frequency 50 Hz is applied to a half wave rectifier using PN diode. No filter is used and the load resistor is `1000 Omega`. The forward resistance `R_(f)` ideal diode is `10 Omega`. Calculate. (i) Peak, average and rms values of load current (ii) d.c power output (ii) a.c power input (iv) % Rectifier efficiency (v) Ripple factor.
A fullwave P.N diode rectifier used load resistor of `1500 Omega`. No filter is used. Assume each diode to have idealized characteristic with `R_(f) = 10 Omega` and `R_(r) = ac`. Since wave voltage applied to each diode has amplitude of 30 volts and frequency 50 Hz. Calculate. (i) Peak, d.c rms load current (ii) d.c power input (iii) A.C power input (iv) Rectifier efficiency.
Figure shows a string of linear mass density `1.0g cm^(-1)` on which a wave pulse is travelling. Find the time taken by pulse in travelling through a distance of `50 cm` on the string. Take `g = 10 ms^(-2)`
Following are equations of four waves : (i) `y_(1) = a sin omega ( t - (x)/(v))` (ii) `y_(2) = a cos omega ( t + (x)/(v))` (iii) `z_(1) = a sin omega ( t - (x)/(v))` (iv) `z_(1) = a cos omega ( t + (x)/(v))` Which of the following statements are correct ?A. One superposition of waves (i) and (iii), a travelling wave having amplitude `a sqrt(2)` will be formed.B. Superposition of waves (ii) and (iii) is not possibleC. On superposition of waves (i) and (ii), a transverse stationary wave having maximum amplitude `a sqrt(2)` will be formed.D. On superposition of waves (iii) and (iv), a transverse stationary wave will be formed.
A parabolic pulse given by equation `y ("in cm") = 0.3 - 0.1(x-5t)^(2) (y ge 0)` travelling in a uniform string. The pulse passes through a boundary beyond which its velocity becomes `2.5 m//s`. What will be the amplitude of pulse in this medium after transmission ?
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=`A. `1.25 sec`B. 1 secC. `(13)/(12) sec`D. none
A person going away from a factory on his scooter at a speed of 36 km/hr listens to the siren of the factory. If the actual frequency of the siren is 700 Hz and a wind is blowing along the direction of the scooter at 36 km//hr, find the observed frequency heard by the person. (Given speed of sound `= 340 m//s`)
A car has two horns having a difference in frequency of 180 Hz. The car is approaching a stationary observer with a speed of `60 ms^(-1)`. Calculate the difference in frequencies of the notes as heard by the observer, If velocity of sound in air is `330 ms^(-1)`.
Two engines pass each other moving in opposite directions with uniform speed of of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 300 m/sec :A. 648 HzB. 450 HzC. 270 HzD. 540 Hz
A person observes a change of 2.5 % in frequency of sound of horn of a car. If the car is approaching forward the person & sound velocity is 320 m/s, then velocity of car in m/s will be approximaterly :-A. 8B. 800C. 7D. 6

The equation of a wave is `y=(x,t)=0.05 sin [(pi)/(2)(10x-40t)-(pi)/(4)]m` find: (a) the wavelength, the frequency and the wave velocity (b) the participle velocity and acceleration at `x=0.5m`and `t = 0.05s`.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment