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Chapter 16: Q35P (page 474)

Two sinusoidal waves of the same frequency travel in the same direction along a string. If,ym1=3.0cm,ym2=4.0cm.蠒1=0,and蠒2=蟺/2radwhat is the amplitude of the resultant wave?

Short Answer

Expert verified

The amplitude of the wave is 5.00 cm

Step by step solution

01

The given data

i) Amplitude of first wave,y1m=3.00cmor0.03m

ii) Amplitude of second wave,y2m=4.00cmor0.04m

iii) The first phase,蠒1=0

iv) The second phase,蠒1=蟺/2

02

Understanding the concept of phase

A phasor is a vector that rotates around its tail which is pivoted at the origin of a coordinate system. Herey1mandy2mrepresents the amplitude of the two waves andymrepresents the amplitude of the resultant wave.

03

Calculation of amplitude


The angle made by the phasor of two corresponding waves is 90掳. Using the Pythagorean Theorem we can write,

ym2=y1m2+y2m2=32+42=25ym=5.00cm

So that the resultant amplitude is 5.00cm

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Most popular questions from this chapter

The following two waves are sent in opposite directions on a horizontal string so as to create a standing wave in a vertical plane:

y1(x,t)=(6.00mm)sin(4.00蟺x-400蟺t)y2(x,t)=(6.00mm)sin(4.00蟺虫+400蟺迟)

within X meters andin seconds. An antinode is located at point A. In the time interval that point takes to move from maximum upward displacement to maximum downward displacement, how far does each wave move along the string?

If a wavey(x,t)=(6.0mm)sin(kx+600rad/st)travels along a string, how much time does any given point on the string take to move between displacementsy=+2.0mmand y=-2.0mm?

Figure 16-32 shows the transverse velocity u versus time t of the point on a string at x = 0 , as a wave passes through it. The scale on the vertical axis is set by us=4.0m/s . The wave has the form y(x,t)=ymsin(kx-蝇t+蠒) . What then is 蠒 ? (Caution:A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of 蝇 into y(x,t)and then plotting the function.)

A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that moves up and down through a distance of 1.00 cm. The motion is continuous and is repeated regularly 120 times per second. The string has linear density 120 g/mand is kept under a tension of 90.0 N. Find the maximum value of (a) the transverse speed uand (b) the transverse component of the tensiont. (c) Show that the two maximum values calculated above occur at the same phase values for the wave. What is the transverse displacement yof the string at these phases? (d) What is the maximum rate of energy transfer along the string? (e) What is the transverse displacement ywhen this maximum transfer occurs? (f) What is the minimum rate of energy transfer along the string? (g) What is the transverse displacement ywhen this minimum transfer occurs?

Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with a speed of10cm/s. If the time interval between instants when the string is flat is0.50s, what is the wavelength of the waves?
See all solutions

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