Mastering Physics 12

This is a complex tone with a fundamental of 400 Hz, plus some of its overtones.

A certain sound contains the following frequencies: 400 Hz, 1600 Hz, and 2400 Hz. Select the best description of this sound. This is a pure tone. This is a complex tone with a fundamental of 400 Hz, plus some of its overtones. This is a complex tone with a virtual pitch of 800 Hz. These frequencies are unrelated, so they are probably pure tones from three different sound sources.

A should be at 90 degrees with same magnitude and B should be at 270 degrees with same magnitude

A long string is stretched and its left end is oscillated upward and downward. Two points on the string are labeled A and B.

They should both be at 0 degrees with the same magnitude

A long string is stretched and its left end is oscillated upward and downward. Two points on the string are labeled A and B.

none of the above

An oscillator creates periodic waves on two strings made of the same material. The tension is the same in both strings. If the strings have the same thickness but different lengths, which of the following parameters, if any, will be different in the two strings? Check all that apply. wave frequency wave speed wavelength none of the above

wave speed wavelength

An oscillator creates periodic waves on two strings made of the same material. The tension is the same in both strings. f the strings have different thicknesses, which of the following parameters, if any, will be different in the two strings? Check all that apply. wave frequency wave speed wavelength none of the above

y(x,0) = 0

At time t=0, what is the displacement of the string y(x,0)? Express your answer in terms of A, k, and other previously introduced quantities.

x1, x2, x3 = 0.500,1,1.50 λ

At which three points x1, x2, and x3 closest to x=0 but with x>0 will the displacement of the string y(x,t) be zero for all times? These are the first three nodal points. Express the first three nonzero nodal points in terms of the wavelength λ. List them in increasing order, separated by commas. You should enter only the factors that multiply λ. Do not enter λ for each one.

It remains zero.

Consider the point where the two pulses start to overlap, point O in (Figure 2) . What is the displacement of point O as these pulses interfere? It varies with time. It remains zero. It depends on the (identical) amplitude of the pulses. It is zero only when the pulses begin to overlap.

vy(x,t)/∂y(x,t)/∂x = −ω/k

Find the ratio of the y velocity of the string to the slope of the string calculated in the previous part. Express your answer as a suitable combination of some of the variables ω, k, and vp.

∂y(x,t)/∂x = Akcos(kx−ωt)

Find the slope of the string ∂y(x,t)∂x as a function of position x and time t. Express your answer in terms of A, k, ω, x, and t.

vp = ω/k

Find the speed of propagation vp of this wave.

λ1, λ2, λ3 = 2L,L,2/3L

Find the three longest wavelengths (call them λ1, λ2, and λ3) that "fit" on the string, that is, those that satisfy the boundary conditions at x=0 and x=L. These longest wavelengths have the lowest frequencies. Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas.

f1, f2, f3 = (1/2)v)/L,v/L,(3/2)v)/L

Find the three lowest normal mode frequencies f1, f2, and f3. Express the frequencies in terms of L, v, and any constants. List them in increasing order, separated by commas.

vy(x,t) = −Aωcos(kx−ωt)

Find the y velocity vy(x,t) of a point on the string as a function of x and t.

B > E = F > A > C > D

Rank each wire-mass system on the basis of its fundamental frequency.

D > A= C= E > B= F

Rank each wire-mass system on the basis of its fundamental wavelength.

E > A = B > C=D=F

Rank each wire-mass system on the basis of its wave speed.

fi = v/λi

The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength λi. Find the frequency fi of the ith normal mode. Express fi in terms of its particular wavelength λi and the speed of propagation of the wave v.

v = 384 m/s

The frequency of the fundamental of the guitar string is 320 Hz. At what speed v do waves move along that string?

C

The given example looks like this: _______/-\_______________/-\________

overtonenumber=patternnumber−1

The standing wave frequencies for this string are f1=320Hz, f2=2f1=640Hz, f3=3f1=960Hz, etc. How does the overtone number relate to the standing wave pattern number, previously denoted with the variable n? overtonenumber=patternnumber overtonenumber=patternnumber+1 overtonenumber=patternnumber−1 There is no strict relationship between overtone number and pattern number.

The wavelength λi can have only certain specific values if the boundary conditions are to be satisfied.

The string described in the problem introduction is oscillating in one of its normal modes. Which of the following statements about the wave in the string is correct? The wave is traveling in the +x direction. The wave is traveling in the -x direction. The wave will satisfy the given boundary conditions for any arbitrary wavelength λi. The wavelength λi can have only certain specific values if the boundary conditions are to be satisfied. The wave does not satisfy the boundary condition yi(0;t)=0.

y(x,T/4) = Asin(kx)

What is the displacement of the string as a function of x at time T/4, where T is the period of oscillation of the string? Express the displacement in terms of A, x, k, and other constants; that is, evaluate ωT/4 and substitute it in the expression for y(x,t).

T = 2π/ω

What is the period T of this wave? Express the period in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π.

ϕ(x,t) = kx−ωt

What is the phase ϕ(x,t) of the wave? Express the phase in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π.

v = ω/k

What is the speed of propagation v of this wave? Express the speed of propagation in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π.

λ1 = 120 cm

What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? Express your answer in centimeters.

λ = 40cm

What is the wavelength λ of the standing wave shown on the guitar string? Express your answer in centimeters.

λ = 2π/k

What is the wavelength λ of the wave? Express the wavelength in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π.

x and t

Which of the following are independent variables? x only t only A only k only ω only x and t ω and t A and k and ω

A and k and ω

Which of the following are parameters that determine the characteristics of the wave? x only t only A only k only ω only x and t ω and t A and k and ω

vx(x,t)=0

Which of the following statements about vx(x,t), the x component of the velocity of the string, is true? vx(x,t)=vp vx(x,t)=vy(x,t) vx(x,t) has the same mathematical form as vy(x,t) but is 180∘ out of phase. vx(x,t)=0

he system can resonate at only certain resonance frequencies fi and the wavelength λi must be such that yi(0;t)=yi(L;t)=0.

Which of the following statements are true? The system can resonate at only certain resonance frequencies fi and the wavelength λi must be such that yi(0;t)=yi(L;t)=0. Ai must be chosen so that the wave fits exactly on the string. Any one of Ai or λi or fi can be chosen to make the solution a normal mode.

This wave is oscillating but not traveling.

Which one of the following statements about such a wave as described in the problem introduction is correct? This wave is traveling in the +x direction. This wave is traveling in the −x direction. This wave is oscillating but not traveling. This wave is traveling but not oscillating.

because a pulse is inverted upon reflection

Why does destructive interference occur when the two pulses overlap instead of constructive interference? because the pulses are traveling in opposite directions because a pulse is inverted upon reflection because the pulses are identical and cancel each other out because constructive interference occurs only when the pulses have the same amplitude