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If you double the wavelength of a wave on a particular string, what happens to the wave speed v and the frequency f? (i) v doubles and f is unchanged; (ii) v is unchanged and f doubles; (iii) v becomes one-half as great and f is unchanged; (iv) v is unchanged and f becomes one-half as great; (v) none of these.
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University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
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- (a) The wavefunction of a wave on a string is y(r, t) = 0.35 sin ( 7(10t - 3x + ( where r and y are in metres and t in seconds. (i) Show that y(x, t) is the superposition of two waves, i.e. one can write y(x, t) = g(r, t) + h(x, t), where you need to find wavefunctions g and h. Given that the linear mass density of the string is 0.075 kg m-1, find (ii) the average rate at which energy is transmitted along the string; and (iii) the energy contained in each cycle of the wave.arrow_forward4. (a) A wave is travelling through air with speed, v = 15 m/s and angular frequency of 0.3 rad/s as shown in Fig. 1. Write down the wave equation and calculate its wavenumber, frequency and time period. 0.44 displacement /mm 0- 2 10 time/ms - 0.4- Fig. 1 (b) Two out of phase harmonic waves are traveling on a string having an amplitude of 0.03 cm. If the resultant wave has an amplitude of 0.09 cm, calculate the phase difference between these two waves.arrow_forward(d)v = 2ghmax A wave traveling on a string has the following wave function, y(x, t) = Asin(kx + wt + p). At time t = 0, the point x 0 has a displacement of y(0,0) = 0, and is moving in the negative y -direction. Which of the following is true about the phase constant and the wave speed direction? (a) o = "/2, and the wave is moving in the negative x-direction. (b)y = "2, and the wave is moving in the positive x-direction. (c) o = n and the wave is moving in the negative x-direction. (d)g = n and the wave is moving in the positive x-direction. 11) %3D %3D %3D %3D Y (90) = Aswyz) =0 or %3D Ao las(4)arrow_forwardThe equation of a wave in the international system SI, which propagates by a string is given by the expression: y(x,t)=0,08cos[2π(2x-4t)] Determine the values of the elongation at a point located 2m from the origin at the instant t=5s.arrow_forwardGiven the transverse equation on water: y(x,t) = (0.502 m) cos (0.00450 m^-1 +6.28 s^-1 t) (a) what is amplitude, wave number, angular frequency, wavelength, and natural frequency? (b) what is the speed of the wave? where is the wave moving? (ex. x, y, or z? positive or negative?) (c) what is the direction of the oscillation of the water volume? (ex. x,y,z?) (d) If a small buoy is floating on the water surface, what is the highest point it will reach relative to the normal water level? (without the wave) (e) If a small buoy is floating on the water surface, what is the fastest speed it can have due to the wave?arrow_forwardA)Why does the speed of a wave change when the amplitude remains the same but the frequency changes? B)Why does the wavelength change when the amplitude remains the same but the frequency changes?arrow_forwardA wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1) Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the value of amplitude A=1.3m.arrow_forwardThis figure shows a sinusoidal wave that is traveling from left to right, in the +x-direction. Assume that it is described by a frequency of 53.5 cycles per second, or hertz (Hz).arrow_forward(a) A wave whose wavelength is 0.500 m is travelling down a 500m long wire whose total mass is 25.0 kg. The wire is under a tension of 2000N. (i) Determine the velocity of the wave on the wire. (ii) Determine the frequency of the wave on the wire . 1. (b) A 750-N person stands on a uniform board of weight 300 N and length 15 metres. The board is supported at each end. If the support force at the right end is 3 times that at the left end, how far is the person from the left end of the board?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
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