We have the 2 wave equations
and
.
At t=1.5 s and x=0 we get
and
.
Since
at this value of x and t we must have
i.e
On simplifying the above equation using the trigonometric relation sin(A-B)=sin A cos B-cos A sin B we obtain:
i.e
i.e
on substituting the value of
and determining
.
i.e.
or
i.e
. This reduces to
.
On solving this quadratic equation we obtain :
i.e
or 290 .
For the y velocities to be opposite in sign at these values of x
and t, we must subtract an additional value of from the above
value of
to obtain the
value of
as the final value of
.
5-2 Written problem: Consider two waves on two side-by-side strings along the x-axis, one of form...
7.1 When there are two traveling waves of the same wavelength and frequency (hence the same velocity) in phase: fA (x, t) A sin(kx- ot) fs (x, t) B sin(kx ot) then it's clear that the actual wave you observe is fa B fA (x, t)+ fs (x, t (A B) sin(kx-ot) due to superposition principle. Namely, you observe the same wave form, except now the amplitude is A+ B. Now consider there are two waves of the same wavelength...
What is the answer for (b) and
(c) ??
Two waves are generated on a string of length 3.2 m to produce a three-loop standing wave with an amplitude of 7.4 cm. The wave speed is 111 m/s. Let the equation for one of the waves be of the form y(x, t) = y_m sin (kx + omega t). In the equation for the other wave, what are y_m, k, omega, and the sign in front of omega?
Chapter 16, Problem 051 Two waves are generated on a string of length 3.8 m to produce a three-loop standing wave with an amplitude of 3.6 cm. The wave speed is 115 m/s. Let the equation for one of the waves be of the form y(x, t) ym sin (kx + at). In the equation for the other wave, what are (a) ym, (b) k, (c) a, and (d) the sign in front of a? (a) Number (b) Number (c)...
Two waves are generated on a string of length 5.4 m to produce a three-loop standing wave with an amplitude of 3.2 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x, t) = ym sin (kx + ωt). In the equation for the other wave, what are (a) ym, (b) k, (c) ω, and (d) the sign in front of ω?
no 1 and 2
Homework 3A: Standing Waves 1. Two waves propagate in one direction on a stretched rope. The frequency of the waves is 120 Hz. Both have the same amplitude of 4 cm and wavelength of 0.04 m. (a) Determine the amplitude of the resultant wave if the two original waves differ in phase by Tm/3? (b) What is the phase difference between the two waves if the amplitude of the resultant wave is 0.05 cm? 2. Two...
A sinusoidal transverse wave of wavelength 19.0 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x = 0 is given in the figure as a function of time t. The scale of the vertical axis is set by ys = 4 cm. The wave equation is to be in the form of y = ym sin(kx - ωt + φ). (a) At t = 0, is a...
Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave: y(x,t) = (11.4 cm) * sin(3.9*x - 53.6 s-1*t + 0.11 rad); with x in meters and t in seconds. What is the phase difference between them?What is their amplitude? What is their period?
At time t = 0 and at position x = 0 m along a string, a traveling sinusoidal wave with an angular frequency of 450 rad/s has displacement y = +4.4 mm and transverse velocity u = -0.71m/s. If the wave has the general form y(x, t) = ym sin(kx - ωt + φ), what is phase constant φ?
1. Two waves are traveling along a rope. The individual waves are de- scribed by hi(t, x) = h2(t, x) = 0.3 cos(8x – 4t) 0.3 cos(7.6x - 3.8t) (a) Write the superposition hi + h, in the form h(t, x) = Acos (į Aku - Awt) cos (Kx – wt) (b) What is the amplitude A of the combined wave? (c) What is the phase velocity of the combined wave? (d) What is the group velocity All of the...
Two waves are generated on a string of length 5.4 m to produce a three-loop standing wave with an amplitude of 3.2 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x, t) = ym sin (kx + ωt). In the equation for the other wave, what are (a) ym the answer is NOT 0.032 m. I need the answer in meter i