University Physics Al no9 Waves Class Number ame I. Choose the Correct Answer 1. A disturbance can be written y(x, t)=(e-t/"). This disturbance (A)Not a traveling wave (B)traveling wave with speed v=a (C)a traveling wave with speed v=alb. (D)Traveling wave with speed v=b on:y(x,1)=( Obviously, this disturbanc aveling wave with speed I=b 2. A traveling wave is of the form y(, =Acos(lr-or)+ Bsin(lr-ar), which can also be written as y(x, n=Dsin(kx-@t-o),where (C) (A)D=A+B (B)D=A+B (C)D=A+B( D)D=A-B 3. Which of the following function is not a solution to the wave equation _1 ay2(D) (A)y=sin cost B)y= tan(x+o) (C)y=x3-6x21+12xt2-83 (D)y=sin( +1)cos(x-t) Solution (A)y=sin cost=-[sin(x+1)+sin(x-1]=f(x+vo)+f(x-vo) (B)y=tan(x+1)=f(x+1) 2)3=f(x-1), (D)y=sin(x +t)cos(x-1=sin 2x-sin 2t]*f(x+t), it is not the solution of the wave uation 4. Two waves travel down the same string. The waves have the same velocity, frequency (o), and wavelength but different phase constants(o>%)and amplitudes(A1>A2). According to the principle of superposition, the resultant wave has a frequency f such that (A) (A)f=fo (B)fo/2<f <fo C)0<f<J(D)f=2f0 Solution According to the principle of superposition, the resultant wave has a same frequency as any single 5. A standing wave occurs on a string when two waves of equal amplitude, frequency, and wavelength move in opposite direction on a string. If the wavelength of two waves is decreased to one-half the original length while the wave speed remains unchanged, then the angular frequency of oscillation of the standing wave willUniversity Physics AI No. 9 Waves Class Number Name I．Choose the Correct Answer 1. A disturbance can be written x b xt b t a y(x,t) (e e e ) 2 2 −( / ) 2 / − = . This disturbance is （ D ） (A) Not a traveling wave. (B) A traveling wave with speed v = a. (C) A traveling wave with speed v = a/b. (D) A traveling wave with speed v = b. Solution: ( , ) ( ) ( ) 2 2 2 2 2 ( ) ( ) ( / ) 2 / y x t e e e e e f x vt b x bt t b x x b xt b t a = = = = − − − − − − − Obviously, this disturbance is a traveling wave with speed v=b. 2. A traveling wave is of the form y(x,t) = Acos(kx −ωt) + Bsin(kx −ωt) , which can also be written as y(x,t) = Dsin(kx −ωt −φ), where （ C ） (A) D = A + B (B) D = A + B (C) 2 2 2 D = A + B (D) D = A − B 3. Which of the following function is not a solution to the wave equation 2 2 2 2 2 1 t y x v y ∂ ∂ = ∂ ∂ ?（ D ） (A) y = sin x cost (B) y = tan(x + t) (C) 3 2 2 3 y = x − 6x t +12xt − 8t (D) y = sin(x + t) cos(x − t) Solution: (A) [sin( ) sin( )] ( ) ( ) 2 1 y = sin xcost = x + t + x − t = f x + vt + f x − vt , (B) y = tan(x + t) = f (x + t), (C) 6 12 8 ( 2 ) ( ) 3 2 2 3 3 y = x − x t + xt − t = x − t = f x − t , (D) [sin 2 sin 2 ] ( ) 2 1 y = sin(x + t)cos(x − t) = x − t ≠ f x ± t , it is not the solution of the wave equation. 4. Two waves travel down the same string. The waves have the same velocity, frequency (f0), and wavelength but different phase constants (φ1>φ2) and amplitudes (A1>A2). According to the principle of superposition, the resultant wave has a frequency f such that （ A ） (A) 0 f = f . (B) 0 2 0 f / < f < f (C) 0 0 < f < f (D) 2 0 f = f Solution: According to the principle of superposition, the resultant wave has a same frequency as any single wave. 5. A standing wave occurs on a string when two waves of equal amplitude, frequency, and wavelength move in opposite direction on a string. If the wavelength of two waves is decreased to one-half the original length while the wave speed remains unchanged, then the angular frequency of oscillation of the standing wave will （ C ）